Richa Sharma

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20182022

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6 papers · 1 filter

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…

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.NT2018

Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations

Kalyan Chakraborty, Azizul Hoque, Richa Sharma

It is well-known that for $p = 1, 2, 3, 7, 11, 19, 43, 67, 163$ , the class number of $Q (- p)$ is one. We use this fact to determine all the solutions of $x^{2} + p^{m} = 4 y^{n}$ …

math.NT2018

On the Diophantine equation $f (x) = 2 f (y)$

Sanjay Bhatter, Richa Sharma

Let $f (x) = x^{2} (x^{2} - 1) (x^{2} - 2) (x^{2} - 3) .$ We prove that the Diophantine equation $f (x) = 2 f (y)$ has no solutions in positive integers $x$ and $y$ , except $(x, y) = (1, 1)$ .

math.NT2018

On the solutions of a Lebesgue - Nagell type equation

Sanjay Bhatter, Azizul Hoque, Richa Sharma

We find all positive integer solutions in $x, y$ and $n$ of $x^{2} + 1 9^{2 k + 1} = 4 y^{n}$ for any non-negative integer $k$ .

Integral solutions of certain Diophantine equation in quadratic fields

On a family of elliptic curves of rank at least 2

On the solutions of certain Lebesgue-Ramanujan-Nagell equations

Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations

On the Diophantine equation f(x)=2f(y)

On the solutions of a Lebesgue - Nagell type equation

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

On the Diophantine equation $f (x) = 2 f (y)$