Problem #PRU-30682

Problems Algebra 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 \(ab \equiv 1 \pmod p\).