2022 SSMO Accuracy Round Problems/Problem 5

Problem

Find the number of ordered pairs $(a, b)$ , where $1\leq a, b\leq 9$ , for which the largest integer $n$ that satisfies $(a-b)^k\equiv a^k-b^k\pmod n$ for all $k\geq 1$ is $ab-b^2$ .

Page

Toolbox

Search

2022 SSMO Accuracy Round Problems/Problem 5

Problem

Solution