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 $a \equiv b \pmod n$."

Ran

8 Dec 2023

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 $3 \not\equiv 5 \pmod 4$.

< Chapter 4.2, Q1 Chapter 4.2, Q3 >

Math Number Theory Solution

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

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