On the p-adic zeros of the Tribonacci sequence

Let (T_n)_n∈Z be the Tribonacci sequence and for a prime p and an integer m let ν_p(m) be the exponent of p in the factorization of m. For p=2 Marques and Lengyel found some formulas relating ν_p(T_n) with ν_p(f(n)) where f(n) is some linear function of n (which might be constant) according to the residue class of n modulo 32 and asked if similar formulas exist for other primes p. In this paper, we give an algorithm which tests whether for a given prime p such formulas exist or not. When they exist, our algorithm computes these formulas. Some numerical results are presented.

Mathematics of Computation 93(347), 2023. 21 pages.

PDF © 2023 American Mathematical Society.