K. Chakraborty

activity

20162026

most citedOn Moments of non-normal number fields

6 citations · 15 across the 15 of their papers we have counts for

collaborators

Showing 2022 · math.NTShow all

4 papers · 2 filters

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

Lehmer sequence approach to the divisibility of class numbers of imaginary quadratic fields

Kalyan Chakraborty, Azizul Hoque

Let $k \geq 3$ and $n \geq 3$ be odd integers, and let $m \geq 0$ be any integer. For a prime number $ℓ$ , we prove that the class number of the imaginary quadratic field $\mathbb{Q…

math.NT2022

Diophantine triples with the property $D (n)$ for distinct $n$

Kalyan Chakraborty, Shubham Gupta, Azizul Hoque

We prove that for every integer $n$ , there exist infinitely many $D (n)$ -triples which are also $D (t)$ -triples for $t \in Z$ with $n \neq = t$ . We also prove that there are infin…

math.NT2022

On a family of elliptic curves of rank at least $2$

Kalyan Chakraborty, Richa Sharma

Let $C_{m} : y^{2} = x^{3} - m^{2} x + p^{2} q^{2}$ be a family of elliptic curves over $Q$ , where $m$ is a positive integer and $p, q$ are distinct odd primes. We study the…

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

Lehmer sequence approach to the divisibility of class numbers of imaginary quadratic fields

Diophantine triples with the property D(n) for distinct n

On a family of elliptic curves of rank at least 2

Diophantine triples with the property $D (n)$ for distinct $n$

On a family of elliptic curves of rank at least $2$