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first k elements of permutation of first n have distinct remainder mod k

Source: Canadian Junior Mathematical Olympiad - CJMO 2021 p2

May 29, 2021

remaindernumber theory

Problem Statement

How many ways are there to permute the first

n

positive integers such that in the permutation, for each value of

k \le n

, the first

k

elements of the permutation have distinct remainder mod

k