10 citations · 40 across the 24 of their papers we have counts for
28 papers
Improved exponent bounds for Erdős--Selfridge curves
Pranabesh Das, Kyle Pratt
Given integers , define the Erdős--Selfridge curve \begin{align*} \mathcal{C}_{k,\ell} : y^\ell = x(x+1)\cdots (x+k-1). \end{align*} Bennett and Siksek proved that i…
Computational results on sums of a prime with squares or cubes
Kenny Applegate, Kyle Pratt
One conjectures that all integers greater than 14 are the sum of an odd prime and two positive squares. We prove that all integers with can be represented in thi…
Utilizing Smoothing Techniques to Bound
Andrew Christensen, Kyle Pratt
We demonstrate an improved explicit upper bound of for using smoothing techniques. Our method sharpens previous bounds relying on the Riemann--Sieg…
Binomial coefficients with divisors avoiding an interval
Hung M. Bui, Slava Naprienko, Kyle Pratt +1
We solve a fifty-year-old conjecture of Erdős and Graham concerning whether the binomial coefficient with must always have a divisor $\le…
Cubes from products of terms in progression with one term missing
Kyle Pratt
Let and be integers. We determine all solutions to the equation \begin{align*} n(n+d)(n+2d)\cdots(n+(i-1)d)(n+(i+1)d) \cdots (n+(k-1)d) = y^3…
On the Lebesgue-Nagell equation
Ethan Katz, Kyle Pratt
We investigate the Lebesgue--Nagell equation in integers with an odd prime. A longstanding folklore conjecture asserts that the only solutions are t…