Hulver's site || fermat

Halving sums of squares

By Alan Crowe (Thu Apr 23, 2009 at 05:10:28 PM EST) fermat (all tags)

My previous diary entry concerned multiplying the sums of squares. Now I try to go the other way, factoring sums of squares. Since this is harder I make little progress, but make an interesting detour to visit the quarter-square multiplier.

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Sums of squares

By Alan Crowe (Fri Apr 17, 2009 at 03:10:33 PM EST) fermat (all tags)

Some numbers can be written as the sum of two squares. For example 113=7²+8² and 205=14²+3².

If we multiply 113×205=23165 is the result a sum of squares? Yes, 23165=146²+43², but why? 146 and 43 seem unrelated to any of 3,7,8,14.

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