Problem #PRU-30682

Problems Number Theory Divisibility Divisibility of a number. General properties Division with remainders. Arithmetic of remainders Fermat's little theorem Methods Pigeonhole principle Pigeonhole principle (other)

14–15 3.0

Problem

Let $p$ be a prime number, and $a$ an integer number not divisible by $p$ . Prove that there is a positive integer $b$ such that $a b \equiv 1 (\mod p)$ .

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