Search Results - "Kihel, Omar"

When Does a Given Polynomial with Integer Coefficients Divide Another? by Ayad, Mohamed, Kihel, Omar, Larone, Jesse

“…Let f and g be polynomials with integer coefficients. In this paper, we improve upon a theorem of Nieto. We show that if the content of g divides the content…”
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On the nonnegative integer solutions of the equation F n ± F m = y a by Kihel, Omar, Larone, Jesse

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On the nonnegative integer solutions of the equation Fn ± Fm = ya by Kihel, Omar, Larone, Jesse

“…In this paper, we study the titular Diophantine equation for a fixed positive integer y ≥ 3 in nonnegative integers m, n, and a. We show that the nonnegative…”
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Powers as Fibonacci sums by Earp-Lynch, Benjamin, Earp-Lynch, Simon, Kihel, Omar, Tiebekabe, P.

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On the nonnegative integer solutions to the equation Fn ± Fm = ya by Kebli, Salima, Kihel, Omar, Larone, Jesse, Luca, Florian

“…In this paper, we study the solutions to the titular Diophantine equation in integers n≥m≥0, y≥2 and a≥2. We show that there are only finitely many of them for…”
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On the nonnegative integer solutions to the equation F ± F = y by Kebli, Salima, Kihel, Omar, Larone, Jesse, Luca, Florian

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Apparent paradoxical partitions in countable sets by Ayad, Mohamed, Kihel, Omar

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Small generators of quadratic fields and reduced elements by Kihel, Omar, Lizotte, Jason

“…Ruppert proved that there is a constant d2 such that every imaginary quadratic number field with discriminant DK has a generator α which satisfies H(α)⩽d2|DK|,…”
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Indices in a Number Field by AYAD, Mohamed, BOUCHENNA, Rachid, KIHEL, Omar

“…LetKbe a number field,Abe its ring of integers andpbe a prime number. In this paper, we define a functionμK(p)which counts the number ofθ̄ ∈ A/pAsuch that the…”
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Denominators of algebraic numbers in a number field by Ayad, Mohamed, Bayad, Abdelmejid, Kihel, Omar

“…For any algebraic number γ, let g(x) be the unique irreducible polynomial with integral coefficients, whose leading coefficient c(γ) is positive, such that…”
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ON PERMUTATION BINOMIALS by AYAD, MOHAMED, BELGHABA, KACEM, KIHEL, OMAR

“…Let 𝔽𝑞 be the finite field of characteristic 𝑝 containing 𝑞 = 𝑝𝑟 elements. Let 𝑓(𝑥) = 𝑎𝑥𝑛 + 𝑥𝑚 be a binomial with coefficients in 𝔽𝑞 and 𝑑 =…”
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When is the ring of integers of a number field coverable? by Ayad, Mohamed, Kihel, Omar

“…A commutative ring R is said to be coverable if it is the union of its proper subrings and said to be finitely coverable if it is the union of a finite number…”
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Solutions of a class of quartic Thue inequalities by He, Bo, Kihel, Omar, Togbé, Alain

“…Let n > 1 be an integer. In this paper, first we show that the quartic Thue equality x 4 − ( n + 1 ) x 3 y − n x 2 y 2 + 2 x y 3 + y 4 = μ can be transformed…”
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The paradox of the infinity by Ayad, Mohamed, Kihel, Omar

“…\textit{Let $E$ be an infinite set on which a property $(\bf P)$ is defined. Suppose that $E=\cup_{i\in I} E_i$ is a partition, where each $E_i$ is infinite…”
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Variants of the Brocard-Ramanujan equation by KIHEL, Omar, LUCA, Florian

“…Dans cet article, nous étudions quelques variations sur l'équation diophantienne de Brocard-Ramanujan. In this paper, we discuss variations on the…”
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Prime rational functions over a field by Goedhart, Eva, Kihel, Omar, Larone, Jesse

“…The aim of this paper is to provide sufficient conditions for when a polynomial or rational function over a field K is prime using its order of vanishing at…”
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Proof of the conjecture of Keskin, Siar and Karaatli by Boumahdi, Rachid, Kihel, Omar, Mavecha, Sukrawan

“…In this paper among other results, we will prove the conjecture of Keskin, Siar and Karaatli on the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$…”
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The number of solutions to $y^2=px(Ax^2+2) by Garici, Tarek, Kihel, Omar, Larone, Jesse

“…In this paper, we find a bound for the number of the positive solutions to the titled equation, improving a result of Togb\'e. As a consequence, we prove a…”
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Groupe des unités pour des extensions diédrales complexes de degré 10 sur Q by KIHEL, Omar

“…Le but de cet article est de montrer qu'un ensemble quelconque de quatre racines des polynômes quintiques p(x) exhibés par H. Darmon forme sous certaines…”
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On Permutation Binomials over Finite Fields by Ayad, Mohamed, Kacem, Belghaba, Kihel, Omar

“…Bull. Aust. Math. Soc. 89 (2014) 112-124 Let $\mathbb{F}_{q}$ be the finite field of characteristic $p$ containing $q = p^{r}$ elements and $f(x)=ax^{n} +…”
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