Azizul Hoque

activity

20162026

most citedA note on certain real quadratic fields with class number upto three

2 citations · 7 across the 23 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

math.NT2020

On the solutions of certain Lebesgue-Ramanujan-Nagell equations

Kalyan Chakraborty, Azizul Hoque, Richa Sharma

We completely solve the Diophantine equation $x^{2} + 2^{k} 1 1^{ℓ} 1 9^{m} = y^{n}$ in integers $x, y \geq 1; k, ℓ, m \geq 0$ and $n \geq 3$ with $g cd (x, y) = 1$ , except the case $2\mid k, 2\nmid…

math.NT2020

Class number one problem for the real quadratic fields $Q (m^{2} + 2 r)$

Azizul Hoque, Srinivas Kotyada

We investigate the class number one problem for a parametric family of real quadratic fields of the form $Q (m^{2} + 4 r)$ for certain positive integers $m$ and $r$ .

math.NT2020

On the exponents of class groups of some families of imaginary quadratic fields

Azizul Hoque

Let $a \geq 1$ and $n > 1$ be odd integers. For a given prime $p$ , we prove under certain conditions that the class groups of imaginary quadratic fields $Q (a^{2} - 4 p^{n})$ …

math.NT2020

On a class of Lebesgue-Ramanujan-Nagell equations

Azizul Hoque

We deeply investigate the Diophantine equation $c x^{2} + d^{2 m + 1} = 2 y^{n}$ in integers $x, y \geq 1, m \geq 0$ and $n \geq 3$ , where $c$ and $d$ are given coprime positive integers such that…

On the solutions of certain Lebesgue-Ramanujan-Nagell equations

Class number one problem for the real quadratic fields Q(m2+2r​)

On the exponents of class groups of some families of imaginary quadratic fields

On a class of Lebesgue-Ramanujan-Nagell equations

Class number one problem for the real quadratic fields $Q (m^{2} + 2 r)$