Doubly regular Diophantine quadruples

For a nonzero integer n, a set of m distinct nonzero integers {a_1,a_2,...,a_m} such that a_i a_j + n is a perfect square for all 1
7 pages, revised version, to appear in Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM