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تسجيل مستخدم جديدFrobenius matrices and a variant of Zolotarevs theorem
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In this paper, with the help of the theory of matrices and finite fields we generalize Zolotarevs theorem to an arbitrary finite dimensional vector space over $mathbb{F}_q$, where $mathbb{F}_q$ denotes the finite field with $q$ elements.
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Let $Lambda(n)$ be the von Mangoldt function, and let $[t]$ be the integral part of real number $t$. In this note, we prove that for any $varepsilon>0$ the asymptotic formula $$ sum_{nle x} LambdaBig(Big[frac{x}{n}Big]Big) = xsum_{dge 1} frac{Lambda(
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In 2012, T. Miyazaki and A. Togb{e} gave all of the solutions of the Diophantine equations $(2am-1)^x+(2m)^y=(2am+1)^z$ and $b^x+2^y=(b+2)^z$ in positive integers $x,y,z,$ $a>1$ and $bge 5$ odd. In this paper, we propose a similar problem (which we c
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Considering $mathbb{Z}_n$ the ring of integers modulo $n$, the classical Fermat-Euler theorem establishes the existence of a specific natural number $varphi(n)$ satisfying the following property: $ x^{varphi(n)}=1%hspace{1.0cm}text{for all}hspace{0.2
cm}xin mathbb{Z}_n^*, $ for all $x$ belonging to the group of units of $mathbb{Z}_n$. In this manuscript, this result is extended to a class of rings that satisfies some mild conditions.
Let $E$ be an elliptic curve over $Q$. It is well known that the ring of endomorphisms of $E_p$, the reduction of $E$ modulo a prime $p$ of ordinary reduction, is an order of the quadratic imaginary field $Q(pi_p)$ generated by the Frobenius element
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