MathDB
Does sequence become periodic?

Source: Baltic Way 2011

November 6, 2011
modular arithmeticleast common multiplealgebra proposedalgebra

Problem Statement

A sequence a1,a2,a3,…a_1,a_2,a_3,\ldots of non-negative integers is such that an+1a_{n+1} is the last digit of ann+an−1a_n^n+a_{n-1} for all n>2n>2. Is it always true that for some n0n_0 the sequence an0,an0+1,an0+2,…a_{n_0},a_{n_0+1},a_{n_0+2},\ldots is periodic?
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