Max A. Alekseyev

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math.NT2026

Computing bounded solutions to linear Diophantine equations with the sum of divisors

Max A. Alekseyev

We propose an efficient computational method for finding all solutions $n \leq U$ to the Diophantine equation $aσ (n) = bn + c$ , where integer coefficient $a, b, c$ and an upper bound…

math.NT2025

Generalization of Ramanujan's formula for sums of half-integer powers of consecutive integers via formal Bernoulli series

Max A. Alekseyev, Rafael Gonzalez, Keryn Loor +2

Faulhaber's formula expresses the sum of the first $n$ positive integers, each raised to an integer power $p \geq 0$ , as a polynomial in $n$ of degree $p + 1$ . Ramanujan expressed thi…

math.NT2025

On the $p$ -adic valuations of values of Legendre polynomials

Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit +1

We prove an explicit formula for the $p$ -adic valuation of the Legendre polynomials $P_{n} (x)$ evaluated at a prime $p$ , and generalize an old conjecture of the third author. We also…

Computing bounded solutions to linear Diophantine equations with the sum of divisors

Generalization of Ramanujan's formula for sums of half-integer powers of consecutive integers via formal Bernoulli series

On the p-adic valuations of values of Legendre polynomials

On the $p$ -adic valuations of values of Legendre polynomials