caa a22 4500 605461910 CHVBK 20210128100245.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10114-015-4491-2 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4491-2 Miyazaki Takafumi Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, 101-8308, Tokyo, Japan aut A remark on Jeśmanowicz' conjecture for the non-coprimality case [Elektronische Daten] [Takafumi Miyazaki] Let a, b, c be relatively prime positive integers such that a 2 + b 2 = c 2. Jeśmanowicz' conjecture on Pythagorean numbers states that for any positive integer N, the Diophantine equation (aN) x + (bN) y = (cN) z has 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. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Diophantine equation nationallicence Pythagorean numbers nationallicence Jeśmanowicz' conjecture nationallicence Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1255-1260 1439-8516 31:8<1255 2015 31 10114 https://doi.org/10.1007/s10114-015-4491-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4491-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Miyazaki Takafumi Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, 101-8308, Tokyo, Japan aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1255-1260 1439-8516 31:8<1255 2015 31 10114