A NOTE ON THE EXPONENTIAL DIOPHANTINE EQUATION (4m(2)+1)(x) + (5m(2)-1)(y) = (3m)(z)

作者：Wang, Jianping^*; Wang, Tingting; Zhang, Wenpeng

来源：Colloquium Mathematicum, 2015, 139(1): 121-126.

DOI：10.4064/cm139-1-7

• exponential Diophantine equation
• generalized Ramanujan-Nagell equations
• positive integer solution

Let m be a positive integer. Using an upper bound for the solutions of generalized Ramanujan-Nagell equations given by Y.Bugeaud and T. N. Shorey, we prove that if 3 inverted iota m, then the equation (4m(2) + 1)(x) + (5m(2) - 1)(y) = (3m)(z) has only the positive integer solution (x, y, z) = (1, 1, 2).

• 出版日期2015
• 单位长安大学