1977 IMO Problems/Problem 5
Problem
Let be two natural numbers. When we divide by , we the the remainder and the quotient Determine all pairs for which
Solution
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: [1]
See Also
1977 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
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