Sums of Two Squares
Theorem. If integers N and M can each be written as the sum of two squares, so can their product!
Example: since 2=12+12 and 34=32+52, their product 68 should be expressible as the sum of two squares.
In fact, 68=82+22. Is there an easy way to figure out what squares the product will be made of?
Yes! This all follows from the very cool formula:
(a2+b2) (c2+d2) = (ac+bd)2 + (ad-bc)2.
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