Give an example to show that a^2 \equiv b^2 (mod n) need NOT

Background

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

Theorems and Corollaries in Elementary Number Theory (Ch 1 - 3)

All theorems and corollaries mentioned in David M. Burton’s Elementary Number Theory are listed by following the book’s order. (7th Edition) (Currently Ch 1 - 3)

RanblogRan

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 >

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