1977 IMO Problems/Problem 5
Let be two natural numbers. When we divide by , we the the remainder and the quotient Determine all pairs for which
Using , we have , or , which implies . If we now assume Wlog that , it follows . If , then , contradicting . But from , thus . It follows , and we get . By Jacobi's two squares theorem, we infer that is the only representation of as a sum of squares. This forces , and permutations.
The above solution was posted and copyrighted by cobbler. The original thread for this problem can be found here: 
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