Shubham Gupta

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math.NT2025

Diophantine tuples and Integral Ideals of $Q (d)$

Kalyan Chakraborty, Shubham Gupta, Krishnarjun Krishnamoorthy

Suppose $n$ is the fundamental discriminant associated with a quadratic extension of $Q$ . We show that for every Diophantine $m$ -tuple ${t_{1}, t_{2}, \dots, t_{m}}$ with t…

math.NT2025

Infinitely Many Counter Examples of a Conjecture of Franušić and Jadrijević

Shubham Gupta

Let $d$ be a square-free integer such that $d \equiv 15 (mod 60)$ and the Pell's equation $x^{2} - d y^{2} = - 6$ is solvable in rational integers $x$ and $y$ . In this paper, we prove t…

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

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…

Diophantine tuples and Integral Ideals of Q(d​)

Infinitely Many Counter Examples of a Conjecture of Franušić and Jadrijević

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

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

Diophantine tuples and Integral Ideals of $Q (d)$

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