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

Source: USAMO 2007

April 26, 2007
AMCUSA(J)MOUSAMOinductionsymmetryalgebrapolynomial

Problem Statement

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.
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