Multiplicities of second order linear recurrences

Authors:
Ronald Alter and K. K. Kubota

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

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Abstract | References | Similar Articles | Additional Information

Abstract: A second order linear recurrence is a sequence of integers satisfying a where *N* and *M* are fixed integers and at least one is nonzero. If *k* is an integer, then the number of solutions of is at most 3 (respectively 4) if and there is an odd prime (respectively *q* = 3) such that and . Further is either infinite or provided that either (i) or (ii) .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0441841-2

Keywords:
Linear recurrence,
*p*-adic numbers,
prime number,
multiplicity,
*p*-adic power series,
companion equation

Article copyright:
© Copyright 1973
American Mathematical Society