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A nice number theory problem.

Source: 2021 China Second Round Olympiad(A1) P2

October 7, 2021
number theoryfunction

Problem Statement

Find a necessary and sufficient condition of a,b,n∈N∗a,b,n\in\mathbb{N^*} such that for S={a+bt∣t=0,1,2,⋯ ,n−1}S=\{a+bt\mid t=0,1,2,\cdots,n-1\}, there exists a one-to-one mapping f:S→Sf: S\to S such that for all x∈Sx\in S, gcd⁡(x,f(x))=1\gcd(x,f(x))=1.
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