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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Multiplicities of second order linear recurrences
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by Ronald Alter and K. K. Kubota PDF
Trans. Amer. Math. Soc. 178 (1973), 271-284 Request permission

Abstract:

A second order linear recurrence is a sequence $\{ {a_n}\}$ of integers satisfying a ${a_{n + 2}} = M{a_{n + 1}} - N{a_n}$ where N and M are fixed integers and at least one ${a_n}$ is nonzero. If k is an integer, then the number $m(k)$ of solutions of ${a_n} = k$ is at most 3 (respectively 4) if ${M^2} - 4N < 0$ and there is an odd prime $q \ne 3$ (respectively q = 3) such that $q|M$ and $q\nmid kN$. Further $M = {\sup _k}{\;_{{\text {integer}}}}m(k)$ is either infinite or $\leq 5$ provided that either (i) $(M,N) = 1$ or (ii) $6\nmid N$.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 178 (1973), 271-284
  • MSC: Primary 10A35; Secondary 10B05
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0441841-2
  • MathSciNet review: 0441841