On the Diophantine equation $a^x+(a+2)^y=z²$ where $a\equiv 5\pmod{42}$: Tatra Mt. Math. Publ. Number Theory and Cryptology '20

Year, pages: 2020, 39 - 42

In this paper, we show that the Diophantine equation

a^x+(a+2)^y = z²,

where $ a\equiv 5 \pmod{42}$ and $ a \in\mathbb{N} $ has no solution in non-negative integers.

Dokchann, R., Pakapongpun, A. 2020. On the Diophantine equation $a^x+(a+2)^y=z²$ where $a\equiv 5\pmod{42}$: Tatra Mt. Math. Publ. Number Theory and Cryptology '20. In Tatra Mountains Mathematical Publications, vol. 77, no.3, pp. 39-42. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0030

Dokchann, R., Pakapongpun, A. (2020). On the Diophantine equation $a^x+(a+2)^y=z²$ where $a\equiv 5\pmod{42}$: Tatra Mt. Math. Publ. Number Theory and Cryptology '20. Tatra Mountains Mathematical Publications, 77(3), 39-42. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0030

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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