IMO 2007 Shortlist N6

Let k be a positive integer. Prove that the number (4k2 − 1)2 has a positive divisor of the form 8kn − 1 if and only if ...

IMO 2007 Shortlist N6

Category: Number Theory

Problem

Let k be a positive integer. Prove that the number (4k2 − 1)2 has a positive divisor of the form 8kn − 1 if and only if k is even. (United Kingdom)