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Make Pythagorean Triples

A Pythagorean triple is a group of three whole numbers (integers) that satisfies the equation a² + b² = c², where c is the measure of the hypotenuse.

Let a = i² - j², b = 2ij, and c = i² + j² where i and j are integers.

Then, a² + b² = (i² - j²)² + (2ij)² = i⁴ - 2i²j² + j⁴ + 4i²j² = i⁴ + 2i²j² + j⁴ = (i² + j²)² = c²