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Last digits of 5^n are in a sequence [IL 1977]

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January 11, 2011
number theory proposednumber theory

Problem Statement

Given any integer m>1m>1 prove that there exist infinitely many positive integers nn such that the last mm digits of 5n5^n are a sequence am,am−1,…,a1=5 (0≤aj<10)a_m,a_{m-1},\ldots ,a_1=5\ (0\le a_j<10) in which each digit except the last is of opposite parity to its successor (i.e., if aia_i is even, then ai−1a_{i-1} is odd, and if aia_i is odd, then ai−1a_{i-1} is even).
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