Functional equation

Find all functions

f : \mathbb{R} \to \mathbb{R}

satisfying

f(x+y) = f(x) + f(y)

for all real

x,y

, given that

f

is monotonic.

Topic: Algebra Difficulty: 4/6 Expected time: ~35 min Progressive hints on Lemma: 3

This is a proof problem — the answer is an argument, not a number. The solution is deliberately not posted here: reading a solution you didn't fight for teaches almost nothing. On Lemma you attempt it cold, take one of the 3 progressive hints only when genuinely stuck, then compare your proof against a full walkthrough and mark yourself with the same rubric a competition coordinator would use.

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Functional equation

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