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Iranian TST 2019, second exam, day 1, problem 1

Source: Iranian TST 2019

April 11, 2019
Iranian TSTTST

Problem Statement

SS is a subset of Natural numbers which has infinite members. S’={xy+yx: x,y∈S, x≠y}S’=\left\{x^y+y^x: \, x,y\in S, \, x\neq y\right\} Prove the set of prime divisors of S’S’ has also infinite members Proposed by Yahya Motevassel
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