Non-Negative Integer Solutions of Some Diophantine Equations

作者：Chotchaisthit Somchit^*

来源：Chiang Mai Journal of Science, 2017, 44(3): 1163-1171.

• exponential diophantine equation

In this paper. it is showen that for any non-negative integers m and n, all non-negatvie integer solutions of the Diophantine equation 43(n)2(x) + 43(y) = z(2m) are the form (3, n, 3(43)(n/2)) if m = 1 and n is even, and it has no solution in the case m not equal 1 or n is odd. It is also shown that all non-negative integer solutios of the Diophantine equation 2(x) + 2(n) 43(y) = z(2m) are the following forms:
(x, y, z)={(1, 0, 2); if m = 1 and n = 1,
(3 + n, 0, 3(2(n/2))); if m = 1 and n is even,
(n-3, 0, 3(2(n-3/2))) and (n, 0, 2(n divided by 1/2));
if m = 1 and n >= 3 is odd,
(n, 0, 2(n+1/2m)); if m > 1, 2m | (n + 1) and n >= 3 is odd,
no solution; otherwise.

• 出版日期2017-7