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NT function with primes

Source: Latvia BW TST 2021 P16

September 26, 2021
functionnumber theory

Problem Statement

A function f:N→Nf:\mathbb{N} \to \mathbb{N} is given. If a,ba,b are coprime, then f(ab)=f(a)f(b)f(ab)=f(a)f(b). Also, if m,km,k are primes (not necessarily different), then f(m+k−3)=f(m)+f(k)−f(3).f(m+k-3)=f(m)+f(k)-f(3). Find all possible values of f(11)f(11).
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