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Iran TST P10

Source: Iranian TST problem 10

April 2, 2022
number theory

Problem Statement

We call an infinite set S⊆NS\subseteq\mathbb{N} good if for all parwise different integers a,b,c∈Sa,b,c\in S, all positive divisors of ac−bca−b\frac{a^c-b^c}{a-b} are in SS. for all positive integers n>1n>1, prove that there exists a good set SS such that n∉Sn \not \in S.
Proposed by Seyed Reza Hosseini Dolatabadi
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