A set of m distinct positive integers S = {a_1, ..., a_m} satisfies the Diophantus property D(n) of order n (a positive integer) if, for all i, j = 1, ..., m with i!=j, a_i a_j + n = b_(i j)^2, the b_(i j)s are integers. The set S is called a Diophantine n-tuple. Diophantine 1-doubles are abundant: (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (1, 8), (3, 8), (6, 8), (7, 9), (8, 10), (9, 11), ... (OEIS A050269 and A050270). Diophantine 1-triples are less abundant: (1, 3, 8), (2, 4, 12), (1, 8, 15), (3, 5, 16), (4, 6, 20), ... (OEIS A050273, A050274, and A050275).

Diophantus