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.
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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