MathCastle
Proof WritingChallengeContrapositive and Contradiction

Contrapositive and Contradiction · Challenge problem

"If 2n−12^n - 1 is prime, then nn is prime" is proved by contrapositive: if n=rsn = rs with 1<r<n1 < r < n, then 2r−12^r - 1 divides 2n−12^n - 1. Using this, what is the smallest prime factor of 215−12^{15} - 1?