The Diophantine equation (m2 + n2)x + (2mn)y = (m + n)2z
2020 ◽
Vol 16
(08)
◽
pp. 1701-1708
Keyword(s):
For fixed coprime positive integers [Formula: see text], [Formula: see text], [Formula: see text] with [Formula: see text] and [Formula: see text], there is a conjecture that the exponential Diophantine equation [Formula: see text] has only the positive integer solution [Formula: see text] for any positive integer [Formula: see text]. This is the analogue of Jésmanowicz conjecture. In this paper, we consider the equation [Formula: see text], where [Formula: see text] are coprime positive integers, and prove that the equation has no positive integer solution if [Formula: see text] and [Formula: see text].
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