Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A property of a class of nonlinear difference equations

Author: F. T. Howard
Journal: Proc. Amer. Math. Soc. 38 (1973), 15-21
MathSciNet review: 0309849
Full-text PDF

Abstract | References | Additional Information

Abstract: Let $ g(n)$ be a rational function of $ n$ whose denominator is divisible by the same power of 2 for each $ n$ and let $ {a_1},{a_2}, \cdots $ be any sequence of rational numbers such that for $ {a_n} = g(n)({a_1}{a_{n - 1}} + {a_2}{a_{n - 2}} + \cdots + {a_{n - 1}}{a_1})$. In this paper we determine the exact power of 2 dividing the denominator of $ {a_n}$ for each $ n$ and prove congruences $ \pmod 4$ and $ \pmod 8$.

References [Enhancements On Off] (What's this?)

Additional Information

Keywords: Nonlinear difference equation, recurrence formula, rational function, congruence, Bernoulli number, Rayleigh function
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society