科研之友
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摘要
In 1956 L. Jesmanowicz conjectured, for any primitive Pythagorean triple (a, b, c) satisfying a(2) + b(2) = c(2), that the equation a(x) + b(y) = c(z) has the unique solution (x, y, z) = (2,2,2) in positive integers x, y and z. This is a famous unsolved problem on Pythagorean numbers. In this paper we broadly extend many of classical well-known results on the conjecture. As a corollary we can verify that the conjecture is true if a - b = +/- 1.
- 出版日期2013-2
