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pro vyhledávání: '"11D61, 11B39"'
We consider the Diophantine equation $7x^{2} + y^{2n} = 4z^{3}$. We determine all solutions to this equation for $n = 2, 3, 4$ and $5$. We formulate a Kraus type criterion for showing that the Diophantine equation $7x^{2} + y^{2p} = 4z^{3}$ has no no
Externí odkaz:
http://arxiv.org/abs/2103.03298
Given odd, coprime integers $a$, $b$ ($a>0$), we consider the Diophantine equation $ax^2+b^{2l}=4y^n$, $x, y\in\Bbb Z$, $l \in \Bbb N$, $n$ odd prime, $\gcd(x,y)=1$. We completely solve the above Diophantine equation for $a\in\{7,11,19,43,67,163\}$,
Externí odkaz:
http://arxiv.org/abs/2001.04736
Autor:
Sahukar, Manasi Kumari, Panda, G. K.
A natural number $n$ is called a repdigit if all its digits are same. In this paper, we prove that Euler totient function of no Pell number is a repdigit with at least two digits. This study is also extended to certain subclass of associated Pell num
Externí odkaz:
http://arxiv.org/abs/1802.05542
Publikováno v:
Monatshefte f\"ur Mathematik, 2018
For an integer $ k\geq 2 $, let $ \{F^{(k)}_{n} \}_{n\geq 0}$ be the $ k$--generalized Fibonacci sequence which starts with $ 0, \ldots, 0, 1 $ ($ k $ terms) and each term afterwards is the sum of the $ k $ preceding terms. In this paper, we find all
Externí odkaz:
http://arxiv.org/abs/1707.07519
This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last
Externí odkaz:
http://arxiv.org/abs/math/0403046
We consider the Diophantine equation $7x^{2} + y^{2n} = 4z^{3}$. We determine all solutions to this equation for $n = 2, 3, 4$ and $5$. We formulate a Kraus type criterion for showing that the Diophantine equation $7x^{2} + y^{2p} = 4z^{3}$ has no no
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d79a8b440f8ded2368da0ca87bf81f3
http://arxiv.org/abs/2103.03298
http://arxiv.org/abs/2103.03298
Given odd, coprime integers $a$, $b$ ($a>0$), we consider the Diophantine equation $ax^2+b^{2l}=4y^n$, $x, y\in\Bbb Z$, $l \in \Bbb N$, $n$ odd prime, $\gcd(x,y)=1$. We completely solve the above Diophantine equation for $a\in\{7,11,19,43,67,163\}$,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81ba37c0d7abcb185ee2e599c1f0f02f
Publikováno v:
Monatshefte für Mathematik
For an integer $ k\geq 2 $, let $ \{F^{(k)}_{n} \}_{n\geq 0}$ be the $ k$--generalized Fibonacci sequence which starts with $ 0, \ldots, 0, 1 $ ($ k $ terms) and each term afterwards is the sum of the $ k $ preceding terms. In this paper, we find all
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8d0d1f413c0c2be245d2168d77cd5a4
http://arxiv.org/abs/1707.07519
http://arxiv.org/abs/1707.07519
Publikováno v:
Annals of Mathematics
Annals of Mathematics, Princeton University, Department of Mathematics, 2006, vol. 163, num. 3, pp.969-1018
Annals of Mathematics, Princeton University, Department of Mathematics, 2006, vol. 163, num. 3, pp.969-1018
This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6a8b9fe149751504110766bb95cda98
https://hal.archives-ouvertes.fr/hal-00101193
https://hal.archives-ouvertes.fr/hal-00101193