Nermine El-Sissi

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20042018

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math.NT2018

Evaluation of Gaussian hypergeometric series using Huff's models of elliptic curves

Mohammad Sadek, Nermine El-Sissi, Arman Shamsi Zargar +1

A Huff curve over a field $K$ is an elliptic curve defined by the equation $a x (y^{2} - 1) = b y (x^{2} - 1)$ where $a, b \in K$ are such that $a^{2} \neq = b^{2}$ . In a similar fashion, a general Huff c…

math.NT2017

On large $F$ -Diophantine sets

Mohammad Sadek, Nermine El-Sissi

Let $F \in Z [x, y]$ and $m \geq 2$ be an integer. A set $A \subset Z$ is called an $(F, m)$ -Diophantine set if $F (a, b)$ is a perfect $m$ -power for any $a, b \in A$ where $a…

math.NT2015

New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

W. M. Abd-Elhameed, Y. H. Youssri, N. El-Sissi +1

We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values…

math.NT2015

Edwards Curves and Gaussian Hypergeometric Series

Mohammad Sadek, Nermine El-Sissi

Let $E$ be an elliptic curve described by either an Edwards model or a twisted Edwards model over $F_{p}$ , namely, $E$ is defined by one of the following equations $x^2+y^2=…

math.NT2013

Partitions with equal products and elliptic curves

Mohammad Sadek, Nermine El-Sissi

Let $a, b, c$ be distinct positive integers. Set $M = a + b + c$ and $N = ab c$ . We give an explicit description of the Mordell-Weil group of the elliptic curve $\displaystyle E_{(M,N)}:y^2-M…

Evaluation of Gaussian hypergeometric series using Huff's models of elliptic curves

On large F-Diophantine sets

New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

Edwards Curves and Gaussian Hypergeometric Series

Partitions with equal products and elliptic curves

On large $F$ -Diophantine sets