Brennan Benfield

collaborators

4 papers

math.NT2025

Integers that are not the sum of positive powers

Brennan Benfield, Oliver Lippard

The generalized Waring problem asks exactly which positive integers cannot be expressed as the sum of $j$ positive $k$ -th powers? Using computational techniques, this paper refines…

math.NT2025

Connecting Zeros in Pisano Periods to Prime Factors of $K$ -Fibonacci Numbers

Brennan Benfield, Oliver Lippard

The Fibonacci sequence is periodic modulo every positive integer $m > 1$ , and perhaps more surprisingly, each period has exactly 1, 2, or 4 zeros that are evenly spaced, which also h…

math.NT2024

Fixed points of K-Fibonacci sequences

Brennan Benfield, Oliver Lippard

A $K$ -Fibonacci sequence is a binary recurrence sequence where $F_{0} = 0$ , $F_{1} = 1$ , and $F_{n} = K \cdot F_{n - 1} + F_{n - 2}$ . These sequences are known to be periodic modulo every positive in…

math.NT2024

End behavior of Ramanujan's taxicab numbers

Brennan Benfield, Oliver Lippard, Arindam Roy

Generalized taxicab numbers are the smallest positive integers that are the sum of exactly $j$ , positive $k$ -th powers in exactly $m$ distinct ways. This paper is considers for whi…

Integers that are not the sum of positive powers

Connecting Zeros in Pisano Periods to Prime Factors of K-Fibonacci Numbers

Fixed points of K-Fibonacci sequences

End behavior of Ramanujan's taxicab numbers

Connecting Zeros in Pisano Periods to Prime Factors of $K$ -Fibonacci Numbers