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Function with primes

Source: BMO 2019, Problem 1

May 2, 2019
functionnumber theoryprime numbers

Problem Statement

Let P\mathbb{P} be the set of all prime numbers. Find all functions f:P→Pf:\mathbb{P}\rightarrow\mathbb{P} such that: f(p)f(q)+qp=f(q)f(p)+pqf(p)^{f(q)}+q^p=f(q)^{f(p)}+p^q holds for all p,q∈Pp,q\in\mathbb{P}.
Proposed by Dorlir Ahmeti, Albania
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