Diophantine m-tuples

A Diophantine quadruple of integers is a set of four integers, such as {1, 3, 8, 120}, with the property that if we multiply any two of them and add 1, the result is a square number. Quadruples like this were first studied in the 3rd century by Diophantus of Alexandria, who noticed that the four rational numbers {1/16, 33/16, 17/4, 105/16} have a simila…