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a_{n+1}=a_n+b_n, where b_n is the last digit of a_n & 5 doesn't divide a_n

Source: All Russian MO 1994 ARO

July 29, 2018
recursiveSequencepower of 2number theory

Problem Statement

Let a1a_1 be a natural number not divisible by 55. The sequence a1,a2,a3,...a_1,a_2,a_3, . . . is defined by an+1=an+bna_{n+1} =a_n+b_n, where bnb_n is the last digit of ana_n. Prove that the sequence contains infinitely many powers of two.
(N. Agakhanov)
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