Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Ajai Choudhry"'
Autor:
Oliver Couto, Ajai Choudhry
Publikováno v:
Acta Arithmetica. 202:43-53
In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation $(x_1^5+x_2^5)(x_3^5+x_4^5)=(y_1^5+y_2^5)(y_3^5+y_4^5)$. Further, we show, using elliptic curves, that there exist infinitely many parametric solutions of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b8128c21f55cf5dfe8297d0cbe3eaec
https://doi.org/10.4064/aa210419-4-7
https://doi.org/10.4064/aa210419-4-7
Publikováno v:
International Journal of Number Theory. 18:905-911
In this paper, we obtain several parametric solutions of the diophantine equation [Formula: see text]. We also show how infinitely many parametric solutions of this equation may be obtained by using elliptic curves.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::719b44961dba3d0f44dcfa3b520c605a
https://doi.org/10.1142/s1793042122500476
https://doi.org/10.1142/s1793042122500476
Autor:
Ajai Choudhry, Arman Shamsi Zargar
We obtain two parametric solutions of the diophantine equation $\phi(x_1, x_2, x_3)=\phi(y_1, y_2, y_3)$ where $\phi(x_1, x_2, x_3)$ is the octic form defined by $\phi(x_1, x_2, x_3)=x_1^8+ x_2^8 + x_3^8 - 2x_1^4x_2^4 - 2x_1^4x_3^4 - 2x_2^4x_3^4$. Th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74866942e7fc7ea3042c4cd48df2871e
http://arxiv.org/abs/2206.14084
http://arxiv.org/abs/2206.14084
Autor:
Ajai Choudhry
Publikováno v:
International Journal of Number Theory. 16:1425-1432
In 1851, Prouhet showed that when [Formula: see text] where [Formula: see text] and [Formula: see text] are positive integers, [Formula: see text], the first [Formula: see text] consecutive positive integers can be separated into [Formula: see text]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3110e0e5fe5087c5a8decf2d1d1fef0b
https://doi.org/10.1142/s179304212050075x
https://doi.org/10.1142/s179304212050075x
Autor:
Ajai Choudhry, Arman Shamsi Zargar
Publikováno v:
Notes on Number Theory and Discrete Mathematics. 26:40-44
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51e12d183452a968bb44acf956d9b1e3
https://doi.org/10.7546/nntdm.2020.26.1.40-44
https://doi.org/10.7546/nntdm.2020.26.1.40-44
Autor:
Ajai Choudhry, Andrew Bremner
Publikováno v:
Periodica Mathematica Hungarica. 80:147-157
First we show that there exist infinitely many distinct cyclic cubic number fields K such that the Fermat cubic $$x^3 + y^3 = z^3$$ has non-trivial points in K. Second, we show that the Fermat quartic $$x^4 + y^4 = z^4$$ can have no non-trivial point
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::026b9e645e392423394f9185cf8072e2
https://doi.org/10.1007/s10998-019-00297-y
https://doi.org/10.1007/s10998-019-00297-y
Autor:
Ajai Choudhry, Arman Shamsi Zargar
In this paper we consider the problem of finding pairs of triangles whose sides are perfect squares of integers, and which have a common perimeter and common area. We find two such pairs of triangles, and prove that there exist infinitely many pairs
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3d7c4c4428de88ea9d66ba852aaca3d2
Autor:
Ajai Choudhry
Publikováno v:
International Journal of Number Theory. 14:2129-2154
In this paper, we present a new method of solving certain quartic and higher degree homogeneous polynomial diophantine equations in four variables. The method can also be applied to some diophantine systems in five or more variables. Under certain co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f3d298c47debe434701ab53de204e03e
https://doi.org/10.1142/s1793042118501282
https://doi.org/10.1142/s1793042118501282
Autor:
Ajai Choudhry
Publikováno v:
International Journal of Number Theory. 13:393-417
In this paper we describe a new method of obtaining ideal solutions of the well-known Tarry–Escott problem, that is, the problem of finding two distinct sets of integers [Formula: see text] and [Formula: see text] such that [Formula: see text], [Fo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6854dee8065eb8fc4546b407184d583e
https://doi.org/10.1142/s1793042117500233
https://doi.org/10.1142/s1793042117500233
Autor:
Ajai Choudhry, Jarosław Wróblewski
Publikováno v:
Acta Arithmetica. 178:87-100
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::de6d0b0c00faea07970218a8b20605b2
https://doi.org/10.4064/aa8574-9-2016
https://doi.org/10.4064/aa8574-9-2016