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On the Conjecture of Jeśmanowicz

Göokhan Soydan, Musa Demirci, Ismail Naci Cangul, Alain Togbé

Abstract



We give a survey on some results covering the last 60 years concerning Jeśmanowicz' conjecture. Moreover, we conclude the survey with a new result by showing that the special Diophantine equation
(20k)^x + (99k)^y = (101k)^z
has no solution other than (x; y; z) = (2; 2; 2).

Keywords


Jeśmanowicz conjecture, exponential Diophantine equation

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