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Set of prime divisors

Source: Iran MO 3rd round 2019 mid-terms - Number theory P2

August 1, 2019

number theory

Problem Statement

Prove that for any positive integers

m>n

, there is infinitely many positive integers

a,b

such that set of prime divisors of

a^m+b^n

is equal to set of prime divisors of

a^{2019}+b^{1398}