Write down two fractions whose product is 2.

Add 2 to each. Keep them improper.

Cross multiply to get two whole numbers.

These numbers are the legs of a Pythagorean triangle!

Prove this always works.

This does not work if one of the fractions is less than or equal to -2.

If equal to -2, then one of the cross-products is 0.

If less than -2, then one (but not both) of the cross-products is negative.

This does appear to work with two negative fractions, both of which are greater than -2.

For instance, -4/3 and -3/2 lead to cross products of 3 and 4.