MathDB

Problem 6

Part of 2016 Switzerland Team Selection Test

Problems(1)

$7^{7^n}+1$ is the product of at least $2n + 3$ primes

Source: USAMO 2007

4/26/2007
Prove that for every nonnegative integer nn, the number 77n+17^{7^{n}}+1 is the product of at least 2n+32n+3 (not necessarily distinct) primes.
AMCUSA(J)MOUSAMOinductionsymmetryalgebrapolynomial