Triples (x,y,z) with 1 < x < y < z and z = y + 3 such that x! y! z! is a square.

6, 7, 10, 3, 47, 50, 4, 47, 50, 26, 321, 324, 13, 349, 352, 18, 439, 442, 26, 2735, 2738

1

Dujella et. al. prove that there are no other solutions with x <= 100. This sequence is probably finite.

T. D. Noe, Plot of 7 triples

A. Dujella, F. Najman, N. Saradha, and T. N. Shorey, Products of three factorials, Publ. Math. Debrecen 85/1-2 (2014), pp. 123-130.

(Mma) (using the code in S001000) Select[t, #[[3]] - #[[2]] == 3 &]

Cf. S001000.

nonn,tabl

T. D. Noe, Apr 19 2017