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- Pell_number abstract "In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12, and 41/29, so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numerators of the same sequence of approximations are half the companion Pell numbers or Pell-Lucas numbers; these numbers form a second infinite sequence that begins with 2, 6, 14, 34, and 82.Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + √2. As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combinatorial enumeration problems.As with Pell's equation, the name of the Pell numbers stems from Leonhard Euler's mistaken attribution of the equation and the numbers derived from it to John Pell. The Pell-Lucas numbers are also named after Édouard Lucas, who studied sequences defined by recurrences of this type; the Pell and companion Pell numbers are Lucas sequences.".
- Pell_number thumbnail Pell_octagons.svg?width=300.
- Pell_number wikiPageExternalLink filep.pdf.
- Pell_number wikiPageExternalLink sellers4.pdf.
- Pell_number wikiPageExternalLink diazbar.pdf.
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- Pell_number wikiPageWikiLink 12_(number).
- Pell_number wikiPageWikiLink 14_(number).
- Pell_number wikiPageWikiLink 169_(number).
- Pell_number wikiPageWikiLink 198_(number).
- Pell_number wikiPageWikiLink 1_(number).
- Pell_number wikiPageWikiLink 29_(number).
- Pell_number wikiPageWikiLink 2_(number).
- Pell_number wikiPageWikiLink 34_(number).
- Pell_number wikiPageWikiLink 400_(number).
- Pell_number wikiPageWikiLink 478_(number).
- Pell_number wikiPageWikiLink 5_(number).
- Pell_number wikiPageWikiLink 6_(number).
- Pell_number wikiPageWikiLink 70_(number).
- Pell_number wikiPageWikiLink 82_(number).
- Pell_number wikiPageWikiLink Acta_Mathematica_Academiae_Paedagogiace_Nyíregyháziensis.
- Pell_number wikiPageWikiLink American_Mathematical_Monthly.
- Pell_number wikiPageWikiLink Annals_of_Mathematics.
- Pell_number wikiPageWikiLink Archive_for_History_of_Exact_Sciences.
- Pell_number wikiPageWikiLink Artemas_Martin.
- Pell_number wikiPageWikiLink Boletín_de_la_Sociedad_Matemática_Mexicana.
- Pell_number wikiPageWikiLink Cassini_and_Catalan_identities.
- Pell_number wikiPageWikiLink Cassinis_identity.
- Pell_number wikiPageWikiLink Category:Integer_sequences.
- Pell_number wikiPageWikiLink Category:Recurrence_relations.
- Pell_number wikiPageWikiLink Closest_rational_approximation.
- Pell_number wikiPageWikiLink Combinatorial_enumeration.
- Pell_number wikiPageWikiLink Continued_fraction.
- Pell_number wikiPageWikiLink Denominator.
- Pell_number wikiPageWikiLink Determinant.
- Pell_number wikiPageWikiLink Diophantine_approximation.
- Pell_number wikiPageWikiLink Enumerative_combinatorics.
- Pell_number wikiPageWikiLink Exponential_growth.
- Pell_number wikiPageWikiLink Fibonacci_Quarterly.
- Pell_number wikiPageWikiLink Fibonacci_number.
- Pell_number wikiPageWikiLink Fraction_(mathematics).
- Pell_number wikiPageWikiLink Glasgow_Mathematical_Journal.
- Pell_number wikiPageWikiLink Golden_ratio.
- Pell_number wikiPageWikiLink If_and_only_if.
- Pell_number wikiPageWikiLink Integer.
- Pell_number wikiPageWikiLink Integers.
- Pell_number wikiPageWikiLink John_Pell.
- Pell_number wikiPageWikiLink Journal_of_Integer_Sequences.
- Pell_number wikiPageWikiLink Journal_of_the_Royal_Asiatic_Society_of_Bengal.
- Pell_number wikiPageWikiLink Leonhard_Euler.
- Pell_number wikiPageWikiLink Lucas_number.
- Pell_number wikiPageWikiLink Lucas_sequence.
- Pell_number wikiPageWikiLink Mathematics.
- Pell_number wikiPageWikiLink Mathematics_Magazine.
- Pell_number wikiPageWikiLink Matrix_(mathematics).
- Pell_number wikiPageWikiLink Mind_(journal).
- Pell_number wikiPageWikiLink Missouri_Journal_of_Mathematical_Sciences.
- Pell_number wikiPageWikiLink Modular_arithmetic.
- Pell_number wikiPageWikiLink Newman–Shanks–Williams_number.
- Pell_number wikiPageWikiLink Newman–Shanks–Williams_prime.
- Pell_number wikiPageWikiLink Octagon.
- Pell_number wikiPageWikiLink Pell_equation.
- Pell_number wikiPageWikiLink Pells_equation.
- Pell_number wikiPageWikiLink Prime_number.
- Pell_number wikiPageWikiLink Pythagorean_theorem.
- Pell_number wikiPageWikiLink Pythagorean_triple.
- Pell_number wikiPageWikiLink Recurrence_relation.
- Pell_number wikiPageWikiLink Right_isosceles_triangle.
- Pell_number wikiPageWikiLink Right_triangle.
- Pell_number wikiPageWikiLink Sequence.
- Pell_number wikiPageWikiLink Silver_ratio.
- Pell_number wikiPageWikiLink Special_right_triangles.
- Pell_number wikiPageWikiLink Square_number.
- Pell_number wikiPageWikiLink Square_root_of_2.
- Pell_number wikiPageWikiLink Square_triangular_number.
- Pell_number wikiPageWikiLink The_Mathematical_Gazette.
- Pell_number wikiPageWikiLink Theon_of_Smyrna.
- Pell_number wikiPageWikiLink Triangular_number.
- Pell_number wikiPageWikiLink Édouard_Lucas.
- Pell_number wikiPageWikiLink File:Pell_octagons.svg.
- Pell_number wikiPageWikiLink File:Pell_right_triangles.svg.
- Pell_number wikiPageWikiLinkText "Companion Pell number".
- Pell_number wikiPageWikiLinkText "Pell number".
- Pell_number wikiPageWikiLinkText "Pell number#Pell-Lucas numbers".
- Pell_number wikiPageWikiLinkText "Pell prime".
- Pell_number wikiPageWikiLinkText "companion Pell numbers".
- Pell_number wikiPageWikiLinkText "side and diameter numbers".
- Pell_number hasPhotoCollection Pell_number.
- Pell_number title "Pell Number".
- Pell_number urlname "PellNumber".
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- Pell_number wikiPageUsesTemplate Template:Metallic_ratios.
- Pell_number wikiPageUsesTemplate Template:Num.