Squares in (12 ++ m2) ⋯⋯ ( n2 ++ m2).

Recently, Cilleruelo proved that the product is a square only for n == 3. In this note, using similar techniques, we prove that for the positive integer m whose divisors are of the form of 4 q++1, the product is not a square for n sufficiently large. As a corollary, we prove that for is not a square for all n. [ABSTRACT FROM AUTHOR]