MathDB

Consider a sequence of positive integers

a_1, a_2, a_3, . . .

such that for

k \geq 2

we have

a_{k+1} =\frac{a_k + a_{k-1}}{2015^i},

where

2015^i

is the maximal power of

2015

that divides

a_k + a_{k-1}.

Prove that if this sequence is periodic then its period is divisible by

3.

Problem Statement