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Field extension of rational numbers
An elementary number is one formalization of the concept of a closed-form number. Roughly speaking, it is a complex number that can be specified using
Elementary_number
Branch of pure mathematics
Elementary number theory studies aspects of integers that can be investigated using elementary methods such as elementary proofs. Analytic number theory,
Number_theory
Number divisible only by 1 and itself
factorization". Elementary number theory (2nd ed.). W.H. Freeman and Co. p. 10. ISBN 978-0-7167-0076-0. Sierpiński, Wacław (1988). Elementary Theory of Numbers
Prime_number
Integer having a non-trivial divisor
ISBN / Date incompatibility (help) Long, Calvin T. (1972), Elementary Introduction to Number Theory (2nd ed.), Lexington: D. C. Heath and Company, LCCN 77-171950
Composite_number
bounded by an iterated exponential function with a bounded number of iterations. Every elementary recursive function can be computed in a time bound of this
ELEMENTARY
Number in {..., –2, –1, 0, 1, 2, ...}
Elementary School Mathematics: New Directions. U.S. Department of Health, Education, and Welfare, Office of Education. p. 42. "entry: whole number".
Integer
Set of residue classes modulo n, relatively prime to n
Pettofrezzo & Byrkit (1970, p. 108) Long, Calvin T. (1972), Elementary Introduction to Number Theory (2nd ed.), Lexington: D. C. Heath and Company, LCCN 77171950
Reduced_residue_system
Natural number
incident, at 2 Colinette Road in Putney. 1729 Koshy, Thomas (2007). Elementary Number Theory with Applications (2nd ed.). Academic Press. p. 340. ISBN 978-0-12-372487-8
1729_(number)
Characterization of how many integers are prime
Paul (July 1949). "On a new method in elementary number theory which leads to an elementary proof of the prime number theorem" (PDF). Proceedings of the
Prime_number_theorem
A prime p divides a^p–a for any integer a
the Fermat primality test and is one of the fundamental results of elementary number theory. The theorem is named after Pierre de Fermat, who stated it
Fermat's_little_theorem
Numbers and the basic operations on them
elementary arithmetic, the successor of a natural number (including zero) is the next natural number and is the result of adding one to that number.
Elementary_arithmetic
Mathematical treatise by Euclid
with their proofs that covers plane and solid Euclidean geometry, elementary number theory, and incommensurability. These include the Pythagorean theorem
Euclid's_Elements
Branch of elementary mathematics
modern number theory include elementary number theory, analytic number theory, algebraic number theory, and geometric number theory. Elementary number theory
Arithmetic
Integer that divides another integer
partially ordered by divisibility, has the Hasse diagram: There are some elementary rules: If a ∣ b {\displaystyle a\mid b} and b ∣ c , {\displaystyle b\mid
Divisor
Result in elementary number theory
In elementary number theory, the lifting-the-exponent lemma provides several formulas for computing the p-adic valuation ν p {\displaystyle \nu _{p}}
Lifting-the-exponent_lemma
How many times a number is divisible by 2
In mathematics, an even number (an integer that is divisible by 2) is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly
Singly_and_doubly_even
2003 mathematics text
Elementary Number Theory, Group Theory and Ramanujan Graphs is a book in mathematics whose goal is to make the construction of Ramanujan graphs accessible
Elementary Number Theory, Group Theory and Ramanujan Graphs
Elementary_Number_Theory,_Group_Theory_and_Ramanujan_Graphs
Thesis on the nature of computability
2026-02-24. Church, Alonzo (May 1935). "An unsolvable problem of elementary number theory. Preliminary report" (PDF). Bulletin of the American Mathematical
Church–Turing_thesis
1980s Unique Country Code (UCC) prefix for EAN identifiers of books
Archived from the original on May 15, 2020. Koshy, Thomas (8 May 2007). Elementary number theory with applications (2nd ed.). Academic Press. p. 265. ISBN 978-0-12-372487-8
Bookland
On prime factors of integer products
fundamental result in elementary number theory. If the premise of the lemma does not hold, that is, if p is a composite number, its consequent may be
Euclid's_lemma
Proof that only uses basic techniques
mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer
Elementary_proof
Algorithm for computing greatest common divisors
ISBN 978-1-4200-6659-3. Ore, O. (1948). Number Theory and Its History. New York: McGraw–Hill. Rosen, K. H. (2000). Elementary Number Theory and its Applications (4th ed
Euclidean_algorithm
Natural number
number of vertices that is planar is K4 and that a(K4) equals 4. Grossnickle, Foster Earl; Reckzeh, John (1968). Discovering Meanings in Elementary School
4
Mathematics taught in primary and secondary school
distribution of prime numbers, are studied in basic number theory, another part of elementary mathematics. Elementary Focus: Abacus LCM and GCD Fractions and Decimals
Elementary_mathematics
Number of dots in a centred dot square
In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center
Centered_square_number
Two numbers without shared prime factors
Oystein (1988) [1948], Number Theory and Its History, Dover, ISBN 978-0-486-65620-5 Rosen, Kenneth H. (1992), Elementary Number Theory and its Applications
Coprime_integers
1979 mass shooting in San Diego, California, U.S.
The Cleveland Elementary School shooting took place on January 29, 1979, at Grover Cleveland Elementary School in San Diego, California, United States
Cleveland Elementary School shooting (San Diego)
Cleveland_Elementary_School_shooting_(San_Diego)
Numbers whose sum of divisors is twice the number plus 1
MR 0569525. S2CID 120459203. Zbl 0425.10005. James J. Tattersall (1999). Elementary number theory in nine chapters. Cambridge University Press. pp. 147. ISBN 0-521-58531-7
Quasiperfect_number
Theorem on prime numbers
Arithemeticae & other papers on number theory) (2nd ed.). New York: Chelsea. ISBN 0-8284-0191-8. Landau, Edmund (1966). Elementary Number Theory. New York: Chelsea
Wilson's_theorem
American mathematician and author
who believe in numerology. Dudley is the author of books including: Elementary Number Theory (1969; 2nd ed. 1978) A Budget of Trisections (1987); revised
Underwood_Dudley
Type of figurate number
Centered polygonal number Polyhedral number Fermat polygonal number theorem See Basel problem. Tattersall, James J. (2005). Elementary Number Theory in Nine
Polygonal_number
Count of the possible partitions of a set
EMS Press. 2001 [1994]. Hurst, Greg; Schultz, Andrew (2009). "An elementary (number theory) proof of Touchard's congruence". arXiv:0906.0696 [math.CO]
Bell_number
Book by David Wells
Interesting Numbers is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in
The Penguin Dictionary of Curious and Interesting Numbers
The_Penguin_Dictionary_of_Curious_and_Interesting_Numbers
Biennial conference series on computational number theory
number theory. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number
Algorithmic Number Theory Symposium
Algorithmic_Number_Theory_Symposium
South African-born mathematician
of Ilya Piatetski-Shapiro (Collected Works), 2000 (joint author) Elementary Number Theory, Group Theory and Ramanujan Graphs, 2003 (joint editor) Selected
Peter_Sarnak
Subatomic particle having no substructure
In the Standard Model of particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles
Elementary_particle
Several textbooks of number theory
ideas. The Vorlesungen cover topics in elementary number theory, algebraic number theory and analytic number theory, including modular arithmetic, quadratic
Vorlesungen über Zahlentheorie
Vorlesungen_über_Zahlentheorie
Math competition
combinatorics, geometry, and number theory. Algebra is restricted to elementary algebra, number theory is restricted to elementary number theory, and geometry
Mathematical_olympiad
Product of numbers from 1 to n
powers". Journal of Number Theory. 9 (4): 452–458. doi:10.1016/0022-314x(77)90006-3. Koshy, Thomas (2007). "Example 3.12". Elementary Number Theory with Applications
Factorial
Area of a right triangle with rational-numbered sides
ISBN 978-0-471-66700-1. Uspensky, J. V.; Heaslet, M. A. (1939). Elementary Number Theory. Vol. 2. McGraw Hill. p. 419. Dickson, Leonard Eugene (1966)
Congruent_number
Type of mathematical function
mathematics, an elementary function is a function of a single variable (real or complex) that is typically encountered by beginners. The basic elementary functions
Elementary_function
Number that is less than the sum of its proper divisors
ISBN 978-981-97-2465-9. "Abundant Number". Retrieved 21 May 2026. Tattersall, James J. (2005). Elementary Number Theory in Nine Chapters (2nd ed.). Cambridge
Abundant_number
Conversion constant for amount of substance
amount of substance and the number of particles that it contains. The particles in question are any designated elementary entity, such as molecules, atoms
Avogadro_constant
Charge carried by one proton or electron
The elementary charge, usually denoted by e, is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 e) or, equivalently
Elementary_charge
2012 mass shooting in Connecticut, US
On December 14, 2012, a mass shooting occurred at Sandy Hook Elementary School in Newtown, Connecticut, United States. The perpetrator, 20-year-old Adam
Sandy Hook Elementary School shooting
Sandy_Hook_Elementary_School_shooting
2022 mass shooting in Texas, U.S.
On May 24, 2022, a mass shooting occurred at Robb Elementary School in Uvalde, Texas, United States. Salvador Ramos, an 18-year-old former student of the
Uvalde_school_shooting
Theorem in number theory
Number Theory, Volumes I and II. New York: Dover Publications. p. 42. ISBN 978-0-486-42539-9. Zbl 1009.11001. Tattersall, James J. (2005). Elementary
Lagrange's theorem (number theory)
Lagrange's_theorem_(number_theory)
United States historic place
The John Marshall Elementary School is a historic elementary school that is located in the Frankford neighborhood of Philadelphia, Pennsylvania. It is
John_Marshall_School
theorem states that n > 1 is prime if and only if (n-1)! is congruent to -1 mod n. Burton, David (2010). Elementary Number Theory (7th ed.). McGraw Hill.
Glossary_of_number_theory
German mathematician (1877–1938)
and delivered a lecture entitled Solved and unsolved problems in elementary number theory in Hebrew on 2 April 1925 during the university's groundbreaking
Edmund_Landau
American mathematician
Properties of Certain Exponential Sums. Davidoff is a coauthor of: Elementary Number Theory, Group Theory and Ramanujan Graphs (with Peter Sarnak and Alain
Giuliana_Davidoff
SI unit of amount of substance
exactly 6.02214076×1023 elementary entities which can be atoms, molecules, ions, ion pairs, or other particles. This number of entities equals 602,214
Mole_(unit)
Desktop operating system based on Ubuntu
Elementary OS (stylized as elementary OS) is a Linux distribution based on Ubuntu LTS. It promotes itself as "thoughtful, capable, and ethical computing"
Elementary_OS
Positive integers that have a property about their divisors
In elementary number theory, a highly powerful number is a positive integer that satisfies a property introduced by the Indo-Canadian mathematician Mathukumalli
Highly_powerful_number
Category of mathematical proof
proof: April 1935: Proof of Alonzo Church ("An Unsolvable Problem of Elementary Number Theory"). His proof was to "...propose a definition of effective calculability
Proof_of_impossibility
Number used for counting
Gary L.; Peterson, Blake E.; Burger, William F. (2013). Mathematics for Elementary Teachers: A contemporary approach (10th ed.). Wiley. ISBN 978-1-118-45744-3
Natural_number
Subfield of mathematics
September 1928. Published in English translation as, "The Grounding of Elementary Number Theory", in Mancosu 1998, pp. 266–273. Hilbert, David; Bernays, Paul
Mathematical_logic
Public school in Jacksonville, Florida, USA
Public School Number Four (later renamed Annie Lytle Elementary School) is an abandoned elementary school in Jacksonville, Florida. It was first established
Public_School_Number_Four
Elementary is an American crime drama created by Robert Doherty and loosely based on Sherlock Holmes and other characters appearing in the works of Sir
List_of_Elementary_episodes
Value that makes no change when added
yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical
Additive_identity
United States historic place
The Overbrook Elementary School building is a historic elementary school located in the Overbrook neighborhood of Philadelphia, Pennsylvania, United States
Overbrook_Elementary_School
Addition of several numbers or other values
CRC Press. p. 196. ISBN 978-1-58488-781-2. Koshy, Thomas (2002). Elementary Number Theory with Applications. Harcourt. p. 12. ISBN 978-0-12-421171-1
Summation
Smallest positive number divisible by two integers
Landau, Edmund (1966), Elementary Number Theory, New York: Chelsea Long, Calvin T. (1972), Elementary Introduction to Number Theory (2nd ed.), Lexington:
Least_common_multiple
Incidents listed here occurred at a variety of institutions, including elementary schools, middle schools, high schools, colleges, universities, and trade
List of school shootings in the United States by death toll
List_of_school_shootings_in_the_United_States_by_death_toll
United States historic place
The Mastery Charter School - Smedley Elementary is an American charter school that is located in the Frankford neighborhood of Philadelphia, Pennsylvania
Smedley_Elementary_School
United States historic place
William Frantz Elementary School is an American elementary school located at 3811 North Galvez Street, New Orleans, Louisiana, 70117. Along with McDonogh
William Frantz Elementary School
William_Frantz_Elementary_School
United States historic place
Bayard Taylor School is a historic elementary school located in the Hunting Park neighborhood of Philadelphia, Pennsylvania. It is part of the School District
Bayard_Taylor_School
American mathematician (1919–1985)
problem, by demonstrating that elementary number theory could be defined in terms of the rationals. (Elementary number theory was already known to be
Julia_Robinson
2025 television crossover event
Elementary and It's Always Sunny in Philadelphia crossover is a two-part fictional crossover event between the ABC workplace comedy Abbott Elementary
Abbott Elementary and It's Always Sunny in Philadelphia crossover
Abbott_Elementary_and_It's_Always_Sunny_in_Philadelphia_crossover
Topics referred to by the same term
are a number of elementary schools named Taft Elementary School: Robert A. Taft Elementary School Taft Elementary School (Arizona) Taft Elementary School
Taft_Elementary_School
American public school in North Carolina
both elementary and high school students and a large auditorium. With the construction of another brick two-story school building ("Elementary Number 2 School";
Cherryville_High_School
Natural number
(seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube. As an early prime number in the series of positive
7
Norwegian mathematician (1899–1968)
analogue of rings of polynomials, are part of this work. In more elementary number theory, Ore's harmonic numbers are the numbers whose divisors have
Øystein_Ore
School in Cheyenne, Wyoming, U.S.
Deming Elementary School is an elementary school in Cheyenne, Wyoming. It is part of the Laramie County School District Number 1. The school was designed
Deming_Elementary_School
17th-century conjecture proved by Andrew Wiles in 1994
MR 0992208. Aczel 1996, p. 69 Singh 2022, p. 105. Koshy, T. (2001). Elementary number theory with applications. New York: Academic Press. p. 544. ISBN 978-0-12-421171-1
Fermat's_Last_Theorem
Length of a shortest cycle contained in the graph
S2CID 122784453. Davidoff, Giuliana; Sarnak, Peter; Valette, Alain (2003), Elementary number theory, group theory, and Ramanujan graphs, London Mathematical Society
Girth_(graph_theory)
Part of the MPEG data encoding protocol
caption). An elementary stream is often referred to as "elementary", "data", "audio", or "video" bitstreams or streams. The format of the elementary stream
MPEG_elementary_stream
Problem of inverting exponentiation in groups
(Report). RFC Editor. doi:10.17487/rfc2409. Rosen, Kenneth H. (2011). Elementary Number Theory and Its Application (6 ed.). Pearson. p. 368. ISBN 978-0321500311
Discrete_logarithm
Abbott Elementary is an American television sitcom created by Quinta Brunson for ABC. It stars Brunson as a second grade teacher at Abbott Elementary, a fictional
List of Abbott Elementary episodes
List_of_Abbott_Elementary_episodes
Set with associative invertible operation
University Press, ISBN 978-0-19-280723-6. Rosen, Kenneth H. (2000), Elementary Number Theory and its Applications (4th ed.), Addison-Wesley, ISBN 978-0-201-87073-2
Group_(mathematics)
For a particle, quotient of its electric charge and the elementary charge
the quantum of electric charge being the elementary charge ( e {\displaystyle e} , constant). The charge number equals the electric charge ( q {\displaystyle
Charge_number
American professor of mathematics
of the Association for Computing Machinery. Stein, William (2009). Elementary Number Theory: Primes, Congruences, and Secrets. New York, NY: Springer Verlag
William_A._Stein
Basic concepts of algebra
common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots
Elementary_algebra
United States historic place
The Kennedy Crossan Academics Plus Elementary School is a historic, American elementary school building in the Burholme neighborhood of Philadelphia, Pennsylvania
Kennedy_Crossan_School
United States historic place
The Joseph Pennell Elementary School is a historic, American elementary school in the Belfield neighborhood of Philadelphia, Pennsylvania. It is part of
Joseph_Pennell_School
United States historic place
The James Logan Elementary School is a historic American elementary school building in the Logan neighborhood of Philadelphia, Pennsylvania. It is part
James_Logan_Elementary_School
Alternative decimal expansion of 1
decimals. An elementary but rigorous proof is given below that involves only elementary arithmetic and the Archimedean property: for each real number, there
0.999...
Power of a prime number
120.09.822. S2CID 12825183. Jones, Gareth A. and Jones, J. Mary (1998) Elementary Number Theory Springer-Verlag London doi:10.1007/978-1-4471-0613-5
Prime_power
Direct product of a p-group and a cyclic group of coprime order
A finite group is an elementary group if it is p-elementary for some prime number p. An elementary group is nilpotent. Brauer's theorem on induced characters
Elementary_group
Characterization by prime factors of sums of two squares
Brahmagupta–Fibonacci identity Dudley, Underwood (1969). "Sums of Two Squares". Elementary Number Theory. W.H. Freeman and Company. pp. 135–139. Sloane, N. J. A. (ed
Sum_of_two_squares_theorem
Number
0 (zero, /ˈziː.roʊ/) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical
0
Elementary school in Vancouver, British Columbia, Canada
Elsie Roy Elementary is a public elementary school located in Yaletown, Downtown Vancouver, that is part of Vancouver School Board District No. 39. It
Elsie_Roy_Elementary_School
(1948). Theory of equations. Uspensky, J. V.; Heaslet, M. A. (1939). Elementary Number Theory. Uspensky, J. V. (1937). Introduction to mathematical probability
J._V._Uspensky
Progression formed by taking the reciprocals of an arithmetic progression
Kürschák-féle elemi számelméleti tétel általánosítása" [Generalization of an elementary number-theoretic theorem of Kürschák] (PDF), Mat. Fiz. Lapok (in Hungarian)
Harmonic progression (mathematics)
Harmonic_progression_(mathematics)
Notation for conserved quantities in physics and chemistry
for a spin quantum number without relying on classical models set the stage for the development of quantum numbers for elementary particles in the remainder
Quantum_number
Matrix which differs from the identity matrix by one elementary row operation
an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices
Elementary_matrix
Concept in model theory
in M. If N is an elementary substructure of M, then M is called an elementary extension of N. An embedding h: N → M is called an elementary embedding of N
Elementary_equivalence
United States historic place
Emlen Elementary School, formerly Eleanor Cope Emlen School of Practice, is a historic elementary school in the Mount Airy neighborhood of Philadelphia
Emlen_Elementary_School
Abbott Elementary is an American television series created by Quinta Brunson for ABC. It stars Brunson as a second grade teacher at Abbott Elementary, a fictional
List of Abbott Elementary characters
List_of_Abbott_Elementary_characters
Number, approximately 1.618
11977215. JSTOR 2690013. MR 0828417. Tattersall, James Joseph (1999). Elementary number theory in nine chapters. Cambridge University Press. p. 28. Sloane
Golden_ratio
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