IMO 2019 Shortlist N5

Let a be a positive integer. We say that a positive integer b is a-good if an b ˘ ´ 1 is divisible by an 1 for all posit...

IMO 2019 Shortlist N5

Category: Number Theory

Problem

Let a be a positive integer. We say that a positive integer b is a-good if an b ˘ ´ 1 is divisible by an 1 for all positive integers n with an ě b. Suppose b is a positive integer such that b is a-good, but b 2 is not a-good. Prove that b 1 is prime. (Netherlands)