A NOTE ON THE DIOPHANTINE EQUATION vertical bar a(x) - b(y)vertical bar = c

作者：He Bo^*; Togbe Alain; Yang Shichun

来源：Mathematica Scandinavica, 2010, 107(2): 161-173.

Let a, b, and c be positive integers. We show that if (a, b) = (N-k - 1, N), where N, k >= 2, then there is at most one positive integer solution (x, y) to the exponential Diophantine equation vertical bar a(x) - b(y)vertical bar = c, unless (N, k) = (2, 2). Combining this with results of Bennett [3] and the first author [6], we stated all cases for which the equation vertical bar(N-k +/- 1)(x) - N-y vertical bar = c has more than one positive integer solutions (x, y).

• 出版日期2010
• 单位南宁师范大学