M. Ibrahim

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math.GM2021

On The Emergence of a New Prime Number And Omega Sequences

Moustafa Ibrahim

This paper highlights the emergence of the Omega sequence in number theory and its connection with the emergence of a new prime number, and also highlights its theoretical applicat…

math.GM2020

New expansions for $x^{n} \pm y^{n}$ in terms of quadratic forms

Moustafa Ibrahim

We prove new theorems for the polynomial expansions of $x^{n} \pm y^{n}$ in terms of the binary quadratic forms $α x^{2} + β x y + α y^{2}$ and $a x^{2} + b x y + a y^{2}$ . The paper gives new ari…

On The Emergence of a New Prime Number And Omega Sequences

New expansions for xn±yn in terms of quadratic forms

New expansions for $x^{n} \pm y^{n}$ in terms of quadratic forms