Azizul Hoque

collaborators

3 papers

math.NT2022

On a conjecture of Franu\v sić and Jadrijevi\' c: Counter-examples

Kalyan Chakraborty, Shubham Gupta, Azizul Hoque

Let $d \equiv 2 (mod 4)$ be a square-free integer such that $x^{2} - d y^{2} = - 1$ and $x^{2} - d y^{2} = 6$ are solvable in integers. We prove the existence of infinitely many quadruples in $…

math.NT2022

Generalized Mersenne Numbers of the form $c x^{2}$

Azizul Hoque

Generalized Mersenne numbers are defined as $M_{p, n} = p^{n} - p + 1$ , where $p$ is any prime and $n$ is any positive integer. Here, we prove that for each pair $(c, p)$ with $c\geq…

math.NT2017

Pell-type equations and class number of the maximal real subfield of a cyclotomic field

Azizul Hoque, Kalyan Chakraborty

We investigate the solvability of the Diophantine equation $x^{2} - m y^{2} = \pm p$ in integers for certain integer $m$ and prime $p$ . Then we apply these results to produce family of maxi…

On a conjecture of Franu\v sić and Jadrijevi\' c: Counter-examples

Generalized Mersenne Numbers of the form cx2

Pell-type equations and class number of the maximal real subfield of a cyclotomic field

Generalized Mersenne Numbers of the form $c x^{2}$