MathDB

Function on integers

Source: Bosnia and Herezegovina TST 2010 problem 3

March 30, 2014

functionalgebra proposedalgebra

Problem Statement

Find all functions

f :\mathbb{Z}\mapsto\mathbb{Z}

such that following conditions holds:

a)

f(n) \cdot f(-n)=f(n^2)

for all

n\in\mathbb{Z}

b)

f(m+n)=f(m)+f(n)+2mn

for all

m,n\in\mathbb{Z}