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3

Part of 2015 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

infinite or not?

Source: Olimpiada Rioplatense 2015-Level 3-Problem 3

7/1/2016
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.
number theoryfactorial