Find all functions f:N \to N such that:
f(f(m+n)) = f(m) + f(n) \forall m,n \in N
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Substitute m=n=a+1: f(f(2a+2))=2f(a+1).
ReplyDeleteSubstitute m=a+2,n=a: f(f(2a+2))=f(a+2)+f(a)
So f(a)+f(a+2)=2f(a+1), or f(a+2)-f(a+1)=f(a+1)-f(a). It follows that f is linear. The rest should be easy. :D