The number of solutions to $y^2=px(Ax^2+2)$
In this paper, we find a bound for the number of the positive solutions to the titled equation, improving a result of Togbé. As a consequence, we prove a conjecture of Togbé in a few cases.
math.NT↗
arXiv subjects
Tarek Garici
Publications and source records attributed to Tarek Garici.
Sur une proprieté des polynômes de Stirling
In this article, we give a positive answer to a question posed in 1960 by D.S. Mitrinović and R.S. Mitrinović (see: D.S. Mitrinović et R.S. Mitrinović, Tableaux qui fournissent des polynômes de Stirling, Publications de la Faculté d'Electronique, série: Mathématiques et physique, 34, (1960).1-23.) concerned the Stirling numbers of the first kind $s(n,k).$ We prove that for all $k\geq 2$ there exist an integer $m_{k}$ and a primitive polynomial $P_{k}(x)$ in $\mathbb{Z}[x]$ such that for all $n\geq k$, $s(n,n-k)=\frac{1}{m_{k}}\binom{n}{k+1}\left(n(n-1)\right) ^{\mathop{\rm mod}\nolimits (k,2)}P_{k}(n)$. Moreover for all $k\geq1$, $P_{2k}(0)=P_{2k+1}(0)$.
math.CO↗