MathDB

3

Part of 2011 Baltic Way

Problems(1)

Does sequence become periodic?

Source: Baltic Way 2011

11/6/2011
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?
modular arithmeticleast common multiplealgebra proposedalgebra