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A Remark on Jesmanowicz' Conjecture for the Non-coprimality Case 被引量:11
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作者 Takafumi MIYAZAKI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第8期1255-1260,共6页
Let a, b, c be relatively prime positive integers such that a^2+ b^2= c^2. Jesmanowicz'conjecture on Pythagorean numbers states that for any positive integer N, the Diophantine equation(aN)x+(b N)y=(cN)zhas n... Let a, b, c be relatively prime positive integers such that a^2+ b^2= c^2. Jesmanowicz'conjecture on Pythagorean numbers states that for any positive integer N, the Diophantine equation(aN)x+(b N)y=(cN)zhas no positive solution(x, y, z) other than x = y = z = 2. In this paper, we prove this conjecture for the case that a or b is a power of 2. 展开更多
关键词 Diophantine equation Pythagorean numbers jesmanowicz conjecture
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