MathDB
0372 functional in Z 3rd edition Round 7 p2

Source:

May 9, 2021
functionalfunctional equation3rd editionalgebranumber theory

Problem Statement

Find all functions f:{1,2,...,n,...}→Zf : \{1, 2, ... , n,...\} \to Z with the following properties (i) if a,ba, b are positive integers and a∣ba | b, then f(a)≥f(b)f(a) \ge f(b); (ii) if a,ba, b are positive integers then f(ab)+f(a2+b2)=f(a)+f(b)f(ab) + f(a^2 + b^2) = f(a) + f(b).
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