Vaishavi Sharma

collaborators

3 papers

math.NT2021

Solving Quadratic and Cubic Diophantine Equations using 2-adic Valuation Trees

Maila Brucal-Hallare, Eva G. Goedhart, Ryan Max Riley +2

For fixed integers $D \geq 0$ and $c \geq 3$ , we demonstrate how to use $2$ -adic valuation trees of sequences to analyze Diophantine equations of the form $x^{2} + D = 2^{c} y$ and $x^3+D=2…

math.CA2020

Filter integrals for orthogonal polynomials

Tewodros Amdeberhan, Adriana Duncan, Victor H. Moll +1

Motivated by an expression by Persson and Strang on an integral involving Legendre polynomials, stating that the square of $P_{2 n + 1} (x) / x$ integrated over $[- 1, 1]$ is always $2$ , w…

math.NT2020

Arithmetic properties of the sum of divisors

Tewodros Amdeberhan, Victor H. Moll, Vaishavi Sharma +1

The divisor function $σ (n)$ denotes the sum of the divisors of the positive integer $n$ . For a prime $p$ and $m \in N$ , the $p$ -adic valuation of $m$ is the highest power…