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f(x^2+f(y))=y^2+f(x) for all x,y \in N_m

Source: 2006 VMEO III Shortlist SL A6 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__viet

October 3, 2021
algebrafunctional equationfunctional

Problem Statement

The symbol NmN_m denotes the set of all integers not less than the given integer mm. Find all functions f:Nm→Nmf: N_m \to N_m such that f(x2+f(y))=y2+f(x)f(x^2+f(y))=y^2+f(x) for all x,y∈Nmx,y \in N_m.
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