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In this paper, we find all solutions of the Diophantine equation  x 2  +  C =  y  n   in integers  x ,  y  ≥ 1,  a ,  b ,  c  ≥ 0,  n  ≥ 3, with gcd( x ,  y ) = 1, when  C = 2  a  3  b  17  c   and  C  = 2  a  13  b  17  c  .

On the Diophantine equation x 2 + C = y n for C = 2 a 3 b 17 c and C = 2 a 13 b 17 c