A note on JeA > manowicz' conjecture concerning primitive Pythagorean triples. II

作者：Deng, M. -J.^*; Guo, J.

来源：Acta Mathematica Hungarica, 2017, 153(2): 436-448.

DOI：10.1007/s10474-017-0751-1

• exponential Diophantine equation
• quartic residue character
• Pythagorean triple
• Jesmanowicz' conjecture

Let be a primitive Pythagorean triple such that m, n are positive integers with , , . In 1956, JeA > manowicz conjectured that the only positive integer solution to the exponential Diophantine equation is x = y = z = 2. Let denote and . Using the theory of quartic residue character and elementary method, we first prove JeA > manowicz' conjecture in the following cases. (i) . (ii) , or , (7,2), (11,14), (15,10) . (iii) , (7,10), (11,6), and . Then, by using the above results, two lemmas that based on Laurent's deep result and computer assistance, for with , we prove the conjecture without any assumption on m.

• 出版日期2017-12
• 单位海南大学