- #1

issacnewton

- 1,012

- 32

- Homework Statement
- Let ##f:\mathbb{Z}\to \mathbb{Z}## be a family of functions following the criterion. $$f(2a) + 2 f(b) = f(f(a+b)) $$. Find the family of functions

- Relevant Equations
- definition of function

Since, both the domain and the range is set of integers, we must have just operations of addition and multiplication only in the function. That means, function should be some kind of a polynomial. Plugging ##a=0## and ##b=0##, I can deduce that ##3 f(0) = f(f(0))##. Also I can deduce that ##3 f(2a) = f(f(3a))##. But after this, I am stuck. So, any guidance will be helpful. This is a math Olympiad question.

Thanks

Thanks