I knew the problems and the solutions so I will leave them for now as problems for the reader, and post a solution in a day or two; hopefully with a litlte of the history.
They are suitable for HS level so everyone is invited. Feel free to submit your solutions.
For any two positive integers X and Y, twice the sum of their squares can be expressed as the sum of two squares. For example 2(42 + 72) = 2(16+49) = 2(65) = 130..but 130 = (112+32)
And the followup??? Prove that three times the sum of two squares can be expressed as the sum of four squares.
Enjoy
1 comment:
The first result is moderately interesting:
(a+b)^2 + (a-b)^2 = 2 (a^2 + b^2)
But the second one is then trivial
(a+b)^2 + (a-b)^2 + a^2 + b^2 = 3 (a^2 + b^2)
Do you have some extra constraints for the second problem to make it non-trivial?
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