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 FranuÅ¡iÄ and JadrijeviÄ

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.NT2024

Diophantine $D (n)$ -quadruples in $Z [4 k + 2]$

Kalyan Chakraborty, Shubham Gupta, Azizul Hoque

Let $d$ be a square-free integer and $Z [d]$ a quadratic ring of integers. For a given $n \in Z [d]$ , a set of $m$ non-zero distinct elements in $\mathb…

Diophantine tuples and Integral Ideals of Q(d​)

Infinitely Many Counter Examples of a Conjecture of FranuÅ¡iÄ and JadrijeviÄ

Diophantine D(n)-quadruples in Z[4k+2​]

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

Infinitely Many Counter Examples of a Conjecture of FranuÅ¡iÄ and JadrijeviÄ

Diophantine $D (n)$ -quadruples in $Z [4 k + 2]$