A property of a class of nonlinear difference equations
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- by F. T. Howard
- Proc. Amer. Math. Soc. 38 (1973), 15-21
- DOI: https://doi.org/10.1090/S0002-9939-1973-0309849-0
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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
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 15-21
- DOI: https://doi.org/10.1090/S0002-9939-1973-0309849-0
- MathSciNet review: 0309849