Pythagorean quadruples

Pythagorean quadruples are sets of four whole numbers (integers) that satisfy the equation \(a^2 + b^2 + c^2 = d^2\). They extend the concept of Pythagorean triples, which involve three numbers where two squared numbers add up to a third squared number (such as 3, 4, 5). In quadruples, three squared numbers sum to another squared number, representing a four-dimensional generalization of the right-angled triangle. These are used in advanced math and geometry to explore relationships involving distances in higher-dimensional spaces.