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.
