科研之友
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摘要
Let (a, b, c) be a primitive Pythagorean triple. In 1956, Jesmanowicz conjectured that the equation a(x) + by = c(z) has the unique solution (x, y, z) = (2, 2, 2) in positive integers. In 2010 Miyazaki proposed a similar problem. He conjectured that if (a, b, c) is again a primitive Pythagorean triple with b even, then the equation c(x) + by = a(z) with x, y and z positive integers has the unique solution (x, y, z) = (1, 1, 2) if c = b + 1 and no solutions if c > b + 1. He also proved that his conjecture is true if c = 1 (mod b). We extend Miyazaki's result to the case c = 1 (mod b/2(ord2) ((b))).
- 出版日期2017-6
