Richa Sharma

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20182026

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math.NT2022

Integral solutions of certain Diophantine equation in quadratic fields

Richa Sharma

Let $K = Q (d)$ be a quadratic field and $O_{K}$ be its ring of integers. We study the solvability of the Diophantine equation $r + s + t = r s t = 2$ in $\ma…

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…

Integral solutions of certain Diophantine equation in quadratic fields

On a family of elliptic curves of rank at least 2

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