Abstract
Consider the two-term recurrence sequence {u n} defined by u o = 0, u 1 = 1 and for all n ≥ 2, where a and b are fixed (rational) integers. Let p be a fixed odd prime such that
. Let ξ be a root of f(x) = x 2 - ax - b in its splitting field K over Q. Let be the ring of algebraic integers in K and P a prime ideal of R lying over (p) in Z. By our assumption (1.1) on p, p is unramified.
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Carlip, W., Jacobson, E., Somer, L. (1998). A Criterion For Stability of Two-Term Recurrence Sequences Modulo Odd Primes. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5020-0_8
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