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
基金Supported by Grant in Aid for JSPS Fellows(Grant No.25484)
文摘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.
基金supported by NSFC(No.10901002)supported by NSFC(No.11126173)+2 种基金the NSF of Anhui Province Education Committee(No.KJ2011Z151)the Research Culture Funds of Anhui Normal University(No.2012xmpy009)Anhui Province Natural Science Foundation(No.1208085QA02)
基金Supported by the NSF of China(10901002)the Research Culture Funds of Anhui Normal University(2012xmpy009)+1 种基金The second author is supported by the NSF of China(11126173)Anhui Province Natural Science Foundation(1208085QA02)
