Alexander R. Povolotsky

collaborators

3 papers

math.NT2026

Frequency Ordered Ratio Families Arising from the Factorization of $p_{m - 1} + 1$

Alexander R Povolotsky

We investigate a ratio sequence derived from the factorization of $p_{m - 1} + 1$ , where $p_{n}$ denotes the $n$ th prime. For each $m \geq 3$ , write $p_{m - 1} + 1 = L_{m} R_{m}$ with $L_{m}$ …

math.CO2026

On Additive Representations of Integers by Binomial Coefficients

Alexander Povolotsky

For a fixed integer $k \geq 0$ , consider representations of positive integers as sums of binomial coefficients of the form $(k n)$ . While exact minimal bounds for the number…

math.CO2025

Recurrence Relations for k-Fold Nested Power Sums

Alexander R. Povolotsky

We consider the $k$ -nested sum of integer powers, $F (n, m, k)$ , defined as repeated partial sums of the classical Faulhaber polynomials. We provide an explicit recurrence relation re…

Frequency Ordered Ratio Families Arising from the Factorization of pm−1​+1

On Additive Representations of Integers by Binomial Coefficients

Recurrence Relations for k-Fold Nested Power Sums

Frequency Ordered Ratio Families Arising from the Factorization of $p_{m - 1} + 1$