# Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q2

My Solution for "Give an example to show that $a^{2} \equiv b^{2} \pmod n$ need not imply that $a \equiv b \pmod n$."

## Table of Contents

Background

All theorems, corollaries, and definitions listed in the book's order:

**I will only use theorems or facts that are proved before this question**. So you will not see that I quote theorems or facts from the later chapters.

## Question

Give an example to show that $a^{2} \equiv b^{2} \pmod n$ need not imply that $a \equiv b \pmod n$.

## Solution

$3^{2} \equiv 5^{2} \pmod 4$, but $3 \not\equiv 5 \pmod 4$.

**Read More:** All My Solutions for This Book

## Related Pages

### Ranblog Newsletter

Join the newsletter to receive the latest updates in your inbox.