IMO 1960, Problem 1

Determine all three-digit numbers

N

that are divisible by

11

and for which

N/11

equals the sum of the squares of the digits of

N

Topic: Number Theory Difficulty: 3/6 Expected time: ~30 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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IMO 1960, Problem 1

Train it on Lemma

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