# Integral Factorial Ratios

Source: [Integral Factorial Ratios](<https://www.sota2.com/research/paper/68fa55861e209131ce994bdc>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T13:37:39.028Z

Authors: K. Soundararajan

Published: 2019-01-16T04:38:52.000Z

## Abstract

This paper describes a new approach to classifying integral factorial ratio, obtaining in particular a direct proof of a result of Bober. These results generalize an observation going back to Chebyshev that $(30n)!n!/((15n)!(10n)!(6n)!)$ is an integer for all $n$. Due to the work of Rodriguez-Villegas and Beukers and Heckman, this problem is closely related to classifying hypergeometric functions with finite monodromy groups, and the result of Bober was originally derived as a consequence of the work of Beukers--Heckman. The new proof is elementary and makes partial progress on other related questions.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1901.05133>)

[PDF](<https://arxiv.org/pdf/1901.05133.pdf>)