In this paper, we prove that for any positive integer p, when p ≡ 1 (mod 6) or, p ≡ 3 (mod 6), the Diophantine equation: 2^pA⁶+B³=C² has infinitely many co-prime integral solutions A, B, C. When p=0, this equation has only four integral solutions with (A, B, C)= (±1, 2, ±3). For other integer values of p, the problem is open.

Tbilisi Mathematical Journal, Vol. 7(1) (2014), pp. 31-36