**Z** be the set of all integers.

Determine all f : **Z** -> **Z** such that, for all integers a, b

IMO 2019 Problem 1

Functional Equation

5 out of 10

Functional Equation and How to Solve Them

Do you really need a hint? Try it first!

This problem needs some patience to play around with the variables to see the beauty of symmetry emerge. Ready for it?

- Prove in
**Z**. - Prove in
**Z**

- Prove in
**Z.** - Prove in
**Z** - Hence prove in
**Z** - Hence prove in
**Z**using [1], [2], [3]

- Prove in
**Z**using induction in [4].

- Use [5] in [2] to prove that or in
**Z**.

- Hence prove that the solution of the functional equation is in
**Z or**in**Z**

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