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infinite or not?

Source: Olimpiada Rioplatense 2015-Level 3-Problem 3

July 1, 2016
number theoryfactorial

Problem Statement

We say an integer number n≥1n \ge 1 is conservative, if the smallest prime divisor of (n!)n+1(n!)^n+1 is at most n+2015n+2015. Decide if the number of conservative numbers is infinite or not.
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