MathDB

Find f(m+n)-f(n)+f(m)+2mn

Source:

November 25, 2019

functionFind all functionsalgebra

Problem Statement

Find the functions

f:\mathbb{Z}\longrightarrow\mathbb{Z}_{\ge 0}

that satisfy the following two conditions:
\text{(a)} f(m+n)=f(n)+f(m)+2mn, \forall m,n\in\mathbb{Z}

\text{(b)} f(f(1))-f(1)

is a perfect square
Marin Ionescu