---
title: "Question in a paper by erdos on divisibility properties of central binomial coefficient"
description: "In this paper by erdos, at the beginning of the proof of theorem $ 1$ he considers the case where both $ \log p$ and $ \log q$ are commensurable numbers(which means that $ p=r^{l}$ and $ q=r^{m}$ )..."
url: https://extraproxies.com/question-in-a-paper-by-erdos-on-divisibility-properties-of-central-binomial-coefficient
date: 2023-10-18
modified: 2023-10-18
author: "ExtraProxies"
tags: ["binomial", "central", "coefficient", "divisibility", "erdos", "paper", "properties", "Question"]
type: post
lang: en
---

# Question in a paper by erdos on divisibility properties of central binomial coefficient

In this paper by erdos, at the beginning of the proof of theorem $ 1$ he considers the case where both $ \log p$ and $ \log q$ are commensurable numbers(which means that $ p=r^{l}$ and $ q=r^{m}$ ) ![enter image description here](https://i.stack.imgur.com/ZUuA8.jpg)

Further states that any sum $ \sum_{i}r^{n_{i}kl}$ has all the digits either $ 0$ or $ 1$ to both the bases $ p$ and $ q$ . I didn’t get this line particularly. Why is he taking $ 0$ and $ 1$ as the digits and what is $ n_{i}$ ?