Problem

Source: USAMO 1991 #3

Tags: induction, modular arithmetic, strong induction, number theory, relatively prime, prime numbers, number theory unsolved



Show that, for any fixed integer n1, the sequence 2,22,222,2222,(modn)is eventually constant. [The tower of exponents is defined by a1=2,ai+1=2ai. Also ai(modn) means the remainder which results from dividing ai by n.]