JEŚMANOWICZ’ CONJECTURE ON PYTHAGOREAN TRIPLES
2017 ◽
Vol 96
(1)
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pp. 30-35
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Keyword(s):
In 1956, Jeśmanowicz conjectured that, for any positive integers $m$ and $n$ with $m>n$, $\gcd (m,n)=1$ and $2\nmid m+n$, the Diophantine equation $(m^{2}-n^{2})^{x}+(2mn)^{y}=(m^{2}+n^{2})^{z}$ has only the positive integer solution $(x,y,z)=(2,2,2)$. In this paper, we prove the conjecture if $4\nmid mn$ and $y\geq 2$.
2016 ◽
Vol 95
(1)
◽
pp. 5-13
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2014 ◽
Vol 90
(1)
◽
pp. 9-19
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2020 ◽
Vol 57
(2)
◽
pp. 200-206
2020 ◽
Vol 16
(08)
◽
pp. 1701-1708
2013 ◽
Vol 90
(1)
◽
pp. 20-27
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2017 ◽
Vol 55
(1)
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pp. 115-118