Chiang Mai Journal of Science

In this paper, it is shown that for any non-negative integers m and n, all non-negative integer solutions of the Diophantine equation 43ⁿ2^x + 43^y = z^2m are the from (3, n, 3(43)) if m = 1 and n is even, and it has no solution in the case m  1 or n is odd. It is also shown that all non-negative integer solutions of the Diophantine equation 2^x + 2ⁿ43^y = z^2m are the following forms: