Question 2
Let $M$ consist of all real-valued functions $f$ defined on the integers such that:
(a) For all integers $x,y$, $f(x)f(y)=f(x+y)+f(x-y)$.
(b) $f(0)\ne0$.
Find all $f\in M$ satisfying $f(1)=5/2$.
(a) For all integers $x,y$, $f(x)f(y)=f(x+y)+f(x-y)$.
(b) $f(0)\ne0$.
Find all $f\in M$ satisfying $f(1)=5/2$.