Problem #PRU-100578

Problems Number Theory Divisibility Divisibility of a number. General properties Divisibility rules

Problem

Denote by $n!$ (called $n$ -factorial) the following product $n! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot . . . \cdot n$ . Show that if $n! + 1$ is divisible by $n + 1$ , then $n + 1$ must be prime. (It is also true that if $n + 1$ is prime, then $n! + 1$ is divisible by $n + 1$ , but you don’t need to show that!)

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