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Number used to approximate the square root of 2
sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that
Pell_number
Solution to x*x + y*y + z*z = 3xyz
+ 1 ) , {\displaystyle (2,P_{2n-1},P_{2n+1}),\,} where Pk is the kth Pell number. Aside from the two smallest singular triples (1, 1, 1) and (1, 1, 2)
Markov_number
Natural number
allowed 107,578,520,350 = 30th Pell number. 109,972,410,221 = number of trees with 32 unlabeled nodes 127,004,500,762 = number of parallelogram polyominoes
100,000,000,000
Natural number
squares in ten different ways. 198 is a Pell–Lucas number. Its corresponding Pell number is 70. "198". NumberADay. Mathematical Association of America
198_(number)
Natural number
Erdős–Woods number, following 22 and 16. It is the ninth Fibonacci number and a companion Pell number. Since it is an odd-indexed Fibonacci number, 34 is a
34_(number)
Natural number
418 : Leyland number using 5 and 13 (513 + 135) 1,311,738,121 : 25th Pell number. 1,382,958,545 : 15th Bell number. 1,392,251,012 : number of secondary
1,000,000,000
Natural number
(seventy) is the natural number following 69 and preceding 71. 70 is a composite number, an Erdős–Woods number, a Pell number, a central binomial coefficient
70_(number)
Natural number
logarithmic number 1,129,30832 + 1 is prime 1,136,689 = Pell number, Markov number 1,174,281 = Fine number 1,185,921 = 10892 = 334 1,200,304 = 17 + 27 + 37 +
1,000,000
Natural number
33rd Pell number, 157th Markov number 1,523,548,331,041 = 1,234,3212 = 1,1114 1,548,008,755,920 : 60th Fibonacci number 1,563,135,350,013 : number of (unordered
1,000,000,000,000
Natural number
sublime numbers, numbers that have a perfect number of divisors whose sum is also perfect. 12 is a Pell number because 17/12 is the closest approximation
12_(number)
Natural number
43-aliquot tree. a companion Pell number. a happy number. palindromic in bases 3 (100013), 9 (1019) and 40 (2240). The sixth magic number. Sloane, N. J. A. (ed
82_(number)
Natural number
triangular number divisible by 1000 195,025 = Pell number, Markov number 196,418 = Fibonacci number, Markov number 196,560 = the kissing number in 24 dimensions
100,000
Natural number
058,681 = Pell number 225,331,713 = self-descriptive number in base 9 232,792,560 = superior highly composite number; colossally abundant number; smallest
100,000,000
Natural number, composite number
in the prime 7-aliquot tree. 14 is the third companion Pell number and the fourth Catalan number. It is the lowest even n {\displaystyle n} for which the
14_(number)
Natural number
Catalan number 36,614,981 = Alternating factorial 38,613,965 = Pell number, Markov number 39,088,169 = Fibonacci number 39,299,897 = Number of trees
10,000,000
On prime divisors in Fibonacci and Lucas sequences
divisor that does not divide any earlier Pell number. The smallest primitive prime divisor of nth Pell number are 1, 2, 5, 3, 29, 7, 13, 17, 197, 41, 5741
Carmichael's_theorem
Natural number
hexagonal number. Like all odd squares, it is a centered octagonal number. 169 is an odd-indexed Pell number, thus it is also a Markov number, appearing
169_(number)
Natural number
a strictly non-palindromic number. 984 = 23 × 3 × 41. 985 = 5 × 197. It is a Markov number, a Pell number, a Smith number, and the sum of three consecutive
900_(number)
Natural number
= 23 × 3 × 17. It is a Pell number, a zero of Mertens function, an Octagonal number, an Untouchable number and a Harshad number. It is the sum of four
400_(number)
Natural number
allowed 13820 = meandric number, open meandric number 13824 = 243 13831 = palindromic prime 13860 = Pell number 13930 = weird number 13931 = palindromic prime
10,000
Natural number
factoriangular number 21,246,581,423,810 : 184th Markov number 21,300,003,689,580 : 36th Pell number 21,440,476,741,631 : 39th Woodall number 21,651,955,485
10,000,000,000,000
Natural number
the natural number following 193 and preceding 195. 194 is the smallest Markov number that is neither a Fibonacci number nor a Pell number. 194 is the
194_(number)
Natural number
556,052 = 28th Pell number. 18,632,325,319 = 33rd Wedderburn–Etherington number. 19,577,194,573 = Markov prime 19,606,122,418 = number of partitions of
10,000,000,000
Natural number
2372 – logarithmic number 2378 – Pell number 2379 – member of the Mian–Chowla sequence 2381 – super-prime, centered square number 2393 – Sophie Germain
2000_(number)
Natural number
pyramidal number 32993 = Leyland prime using 2 & 15 (215 + 152) 33461 = Pell number, Markov number 33511 = square pyramidal number 33781 = octahedral number 34560
30,000
Type of Diophantine equation
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x 2 − n y 2 = 1 , {\displaystyle x^{2}-ny^{2}=1,} where
Pell's_equation
Natural number
number after 79,999 and before 80,001. 80,000 = Since January 2024, the daily URL save limit for YouTube for the Wayback Machine 80,782 = Pell number
80,000
790738119649411319, 18987964267331664557 (OEIS: A049575) Primes in the Pell number sequence P0 = 0, P1 = 1, Pn = 2Pn−1 + Pn−2. 2, 5, 29, 5741, 33461, 44560482149
List_of_prime_numbers
Australian Catholic cardinal (1941–2023)
George Pell (8 June 1941 – 10 January 2023) was an Australian cardinal of the Catholic Church. He served as the inaugural prefect of the Secretariat for
George_Pell
U.S. federal student aid subsidy
A Pell Grant is a subsidy the U.S. federal government provides for students who need it to pay for college. Federal Pell Grants are limited to students
Pell_Grant
British mathematician (1611–1685)
John Pell (1 March 1611 – 12 December 1685) was an English mathematician and political agent abroad. He was made Royal Chair of Mathematics at Orange College
John_Pell_(mathematician)
German guitarist (born 1960)
eponymous band Axel Rudi Pell, working with a number of vocalists; the longest-serving, since 1998, being Johnny Gioeli of Hardline. Pell began his musical career
Axel_Rudi_Pell
Hill Station in Sikkim, India
Pelling (པད་གླིང་། ) is a hill station in ( རྒྱལ་ཤིང་རྫོང་།) Gyalshing district of Sikkim, India. Pelling is nestled at an altitude of 2,150 m (7,050 ft)
Pelling
Gives a finite bound on pairs of consecutive smooth numbers
finding all such pairs using Pell equations. It follows from the Thue–Siegel–Roth theorem that there are only a finite number of pairs of this type, but
Størmer's_theorem
Sum of a factorial number and a triangular number
proved by Ruiz and Luca. A Pell factoriangular number is a number that is both a Pell number and a factoriangular number. Luca and Gómez-Ruiz proved
Factoriangular_number
Branch of pure mathematics
and Pell's equation. He made the first steps towards analytic number theory. Three European contemporaries continued the work in elementary number theory
Number_theory
Engineering consultancy
Pell Frischmann (PF) is a multi-disciplinary engineering consultancy based in London that provides structural and civil engineering, planning, design,
Pell_Frischmann
American politician (1884–1961)
Herbert Claiborne Pell Jr. (February 16, 1884 – July 17, 1961) was a United States representative from New York, U.S. Minister to Portugal, U.S. Minister
Herbert_Pell
Cultural and historic region of England
Latter-day Saints (the Mormons). Pell's equation and the Pell number are both named after 17th century mathematician John Pell. Pell is sometimes credited with
Sussex
Type of prime number conjectured to exist
(mod m) and Tn denotes the n-th tribonacci number. No tribonacci–Wieferich prime exists below 1011. A Pell–Wieferich prime is a prime p satisfying p2
Wall–Sun–Sun_prime
2020 judgment of the High Court of Australia
Pell v The Queen was a High Court of Australia decision that overturned the conviction of Cardinal George Pell for sexual offences against a child. On
Pell_v_The_Queen
Number used for counting
natural-number results: subtracting a larger natural number from a smaller one results in a negative number and dividing one natural number by another
Natural_number
City in Alabama, United States
Pell City is a city in and one of the county seats of St. Clair County, Alabama, United States, the other seat being Ashville. At the 2020 census, the
Pell_City,_Alabama
Numbers obtained by adding the two previous ones
numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have Pn = 2Pn−1 + Pn−2.
Fibonacci_sequence
Historic house in the Bronx, New York
The Bartow–Pell Mansion is a historic house museum at Shore Road in the northern section of Pelham Bay Park, within the New York City borough of the Bronx
Bartow–Pell_Mansion
Integer having a non-trivial divisor
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly, it is a positive integer that has
Composite_number
Historic house in New York, United States
Pelhamdale, also known as The Old Stone House of Philip Pell II, is a historic home located in Pelham Manor, Westchester County, New York. It was built
Pelhamdale
Archbishop of Canterbury. Pell's equation and the Pell number are both named after 17th century mathematician John Pell. Pell is sometimes credited with
Culture_of_Sussex
Integer that is both a perfect square and a triangular number
{\displaystyle (x_{k},y_{k})} to the Pell equation for n = 8 {\displaystyle n=8} yields a square triangular number and its square and triangular roots
Square_triangular_number
Rope-controlled descent
abseilen 'to rope down'), also known as rappelling (/ˈræpɛl/ RAP-pell or /rəˈpɛl/ rə-PELL; from French rappeler 'to recall, to pull through'), is the controlled
Abseiling
Number divisible only by 1 and itself
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that
Prime_number
Prime number of the form 2^n – 1
mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer
Mersenne_prime
Number equal to the sum of its proper divisors
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number
Perfect_number
Figurate number
The triangular lattice representing the n {\displaystyle n} th triangular number contains n {\displaystyle n} rows: the first row contains one point, the
Triangular_number
British web series
British adult puppet comedy horror web series created by Becky Sloan and Joe Pelling that consists of six short episodes released on YouTube between 29 July
Don't_Hug_Me_I'm_Scared
American actor (born 1947)
whom he has two children. In 2014, Jenkins and his wife Sharon received the Pell Award for Lifetime Achievement from Trinity Repertory Company in Providence
Richard_Jenkins
them. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may be included in the list based on their mathematical
List_of_numbers
Positive integer of the form (2^(2^n))+1
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form: F n
Fermat_number
President of the United States from 2021 to 2025
expenditures picked up. When he completed that role in February 2011, he said the number of fraud incidents with stimulus monies had been less than one percent.
Joe_Biden
Australian actor and screenwriter (born 1971)
Matrix Reloaded and The Matrix Revolutions, and Immortan Joe and Rizzdale Pell in Furiosa: A Mad Max Saga. Hulme was born in Melbourne, Victoria where he
Lachy_Hulme
Education policy scholar
executive, scholar, and education policy expert. Known as the "mother of the Pell Grant" because of her work lobbying for its creation, she was national vice
Lois_Rice
British singer (born 1999)
Archived from the original on 26 January 2026. Retrieved 26 January 2026. Pell, Miranda; Maidment, Adam (26 March 2026). "MOBO 2026 winners in full as Olivia
Olivia_Dean
negative Pell equation", Annals of Mathematics, 2 (3): 2035–2104, doi:10.4007/annals.2010.172.2035, MR 2726105 Neukirch, Jürgen (1999), Algebraic Number Theory
Fundamental unit (number theory)
Fundamental_unit_(number_theory)
1958 film from the USA directed by Dick Powell
pilots is a new replacement, talented but brash Lieutenant Ed Pell. On his first mission, Pell abandons his element leader to go after a group of MiG-15s
The_Hunters_(1958_film)
Product of an integer with itself
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with
Square_number
American mathematician (1927–2010)
Selfridge, J. L. (1982). "Polygonal products of polygonal numbers and the Pell equation". Fibonacci Quarterly. 20 (1): 24–28. MR 0660755. Erdos, P; Selfridge
John_Selfridge
British novelty candidate (born 1980)
a trash can as the UK populist leader's election gamble backfires". CNN. Pell, Miranda (7 July 2026). "Count Binface to stand against Farage in Clacton
Count_Binface
Figurate number
"Pentagonal Square Triangular Number". MathWorld. Wolfram. Retrieved April 2, 2025. Anglin, W.S. (1996). "Simultaneous Pell Equations". Math. Comput. 65
Pentagonal_number
Number, non-palindrome after repeated sum with reverse
numbers exist? More unsolved problems in mathematics A Lychrel number is a natural number that cannot form a palindrome through the iterative process of
Lychrel_number
British adult puppet comedy horror television series
2022 British adult puppet comedy horror television series created by Joe Pelling, Becky Sloan and Baker Terry, and produced by Blink Industries. It was
Don't Hug Me I'm Scared (TV series)
Don't_Hug_Me_I'm_Scared_(TV_series)
Natural number
fifth primorial prime, the sixth Sophie Germain prime, a Lucas prime, a Pell prime, and an Eisenstein prime with no imaginary part and real part of the
29_(number)
Spanish communist militant and Soviet agent
Gregorio (7 April 2013). "Caritat Mercader, una revolucionària amb sabates de pell de serp" (in Catalan). Ara. Retrieved 2023-12-14. Mercader & Sánchez 1990
Caridad_Mercader
Infinite integer series where the next number is the sum of the two preceding it
numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47
Lucas_number
Centered figurate number that represents a nonagon with a dot in the center
Encyclopedia of Integer Sequences. OEIS Foundation. Koshy, Thomas (2014), Pell and Pell–Lucas Numbers with Applications, Springer, p. 90, ISBN 9781461484899
Centered_nonagonal_number
American comedian and screenwriter
Audible in April 2020. The voice cast includes Paul Rudd, Jack McBrayer, Paula Pell and Jane Krakowski. In 2020, Lutz starred in, co-wrote, and executive produced
John_Lutz
this sequence is half the corresponding term in the sequence of companion Pell numbers. These numbers also appear in the continued fraction convergents
Newman–Shanks–Williams_prime
Recursive integer sequence
they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients
Catalan_number
Two raised to an integer power
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with the number two as the base and integer n as
Power_of_two
Diplomacy Championship occurs once every two years, rotating between a number of Diplomacy websites. The winner is considered to be the World Champion
International prize list of Diplomacy
International_prize_list_of_Diplomacy
Skyscraper in Manhattan, New York
detailing of its terra-cotta work, but questioned the practicality of its large number of windows: "[The tenant] can, perhaps, find wall space within for one roll
Flatiron_Building
Formula in number theory
{\displaystyle \chi } . For d > 0, let t > 0, u > 0 be the solution to the Pell equation t 2 − d u 2 = 4 {\displaystyle t^{2}-du^{2}=4} for which u is smallest
Class_number_formula
Numbers with a certain property involving recursive summation
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance
Happy_number
List of Scout camps
and was located on the Coosa River. Camp McKenzie Birmingham Area Council Pell City Sold Camp Westmoreland Greater Alabama Council Florence Closed First
List of council camps (Boy Scouts of America)
List_of_council_camps_(Boy_Scouts_of_America)
1988 American crime thriller film by Alan Parker
pick him up and interrogate him. Anderson and Pell tussle at the local barbershop in retaliation for Pell attacking his wife, Anderson takes off presently
Mississippi_Burning
Outdoor swimming pool in Lewes, East Sussex, England
Pells Pool is a public outdoor swimming baths or lido in Lewes, East Sussex, England. The original structure was built in 1860 making it the oldest freshwater
Pells_Pool
Mathematical models of strategic interactions
February 2023. Retrieved 3 February 2023. Genesereth, Michael; Love, Nathaniel; Pell, Barney (15 June 2005). "General Game Playing: Overview of the AAAI Competition"
Game_theory
American football player and coach (born 1957)
Georgia, Colquitt County High School in Moultrie, Georgia, Pell City High School in Pell City, Alabama, and Hoover High School in Hoover, Alabama. Propst
Rush_Propst
American rock band
Pell Mell was an instrumental rock combo, formed in 1980 in Portland, Oregon. The band was formed by Arni May, guitar, and Jon-Lars Sorenson, bass, from
Pell_Mell_(band)
2025 legislation in the United States
limit of $257,000; Restructures income-based repayment programs; and Expands Pell Grants to cover workforce-training programs. A 529 plan will be allowed to
One_Big_Beautiful_Bill_Act
Area of a right triangle with rational-numbered sides
(2008). "The Congruent Number Problem" (PDF). University of Connecticut. Izadi, Farzali (2010-12-30). "Congruent Numbers Via the Pell Equation and its Analogous
Congruent_number
Base-dependent property of integers
In mathematics, a natural number in a given number base is a p {\displaystyle p} -Kaprekar number if the representation of its square in that base can
Kaprekar_number
Iterative algorithm on numbers
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with
Kaprekar's_routine
Political party in the United States
education by increasing state funding for student financial aid such as Pell Grants and college tuition tax deductions. Democrats believe that the government
Democratic Party (United States)
Democratic_Party_(United_States)
In mathematics, specifically in number theory, a Cunningham number is a certain kind of integer named after English mathematician A. J. C. Cunningham.
Cunningham_number
Award
Stanley Pegg, Foreman Electrician, Broady & Son Ltd. George Frederick Pelling, Works Foreman, C. E. Welstead Ltd. Rhoda Kathleen Penn, Temporary Postwoman
1946 New Year Honours (British Empire Medal)
1946_New_Year_Honours_(British_Empire_Medal)
American actor (born 1950)
Circle Repertory Company. During the early 1970s, Dourif appeared in a number of plays, off-Broadway and at Woodstock, New York, including The Ghost Sonata
Brad_Dourif
Root of a quadratic polynomial with a unit leading coefficient
integers occur in the solutions of many Diophantine equations, such as Pell's equations, and other questions related to integral quadratic forms. The
Quadratic_integer
Building in Manhattan, New York
Manhattan Admiral David Glasgow Farragut Gravesite Alice Austen House Bartow–Pell Mansion Bronx Community College Brooklyn Bridge Brooklyn Heights Center for
Brown_Building_(Manhattan)
American singer and actress (born 1969)
Archived from the original on October 4, 2013. Retrieved October 4, 2013. Pell, Michael (February 24, 2015). "Exclusive! Watch Jennifer Lopez's Cute 'Feel
Jennifer_Lopez
Natural number
to how the decimal expansion of 1/89 gives Fibonacci numbers, 1/79 gives Pell numbers, that is, 1 79 = ∑ n = 1 ∞ P ( n ) × 10 − ( n + 1 ) = 0.0126582278
79_(number)
PELL NUMBER
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PELL NUMBER
PELL NUMBER
PELL NUMBER
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PELL NUMBER
PELL NUMBER