Sunday, 6 February 2011
Sums of Squares Problems
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.