IMO 1981, Question 3

I had a great time solving the following question a couple of nights back. More so because I’d failed to solve this question in the past.

This question is completely unapproachable if you try to use algebra. However, generating simple examples helps.

Let me try and write down some solutions to (n^2-mn-m^2)^2=1: they are (1,2), (2,3), (3,5), (5,8)... Do you see a pattern? The answer becomes a two-liner as soon as you observe this.

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Graduate student

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