# Understand the problem

Find all functions satisfying following condition:

##### Source of the problem

IMO longlist 1977

##### Topic

Functional equations

##### Difficulty Level

Medium

##### Suggested Book

Functional Equations by B J Venkatachala

# Start with hints

Do you really need a hint? Try it first!

Prove (by induction on ) that if then .

Note that hint 1 implies that .

Note that hint 2 implies that , i.e. .

Hint 3, combined with hint 1 gives for all .

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