A professor asked me the following question:

"Is $2$ a primitive root $(\text{mod }15)$? Explain."

This is what I wrote:

"It is not because $\varphi(15)=8\neq2$."

He took one point off and replaced my $2$ with a $4$.

I'm confused: why did he do this?

Question

A professor asked me the following question:

"Is $2$ a primitive root $(\text{mod }15)$? Explain."

This is what I wrote:

"It is not because $\varphi(15)=8\neq2$."

He took one point off and replaced my $2$ with a $4$.

I'm confused: why did he do this?

kinggeorge · Answer

He did this because $2^4 \equiv 1 \mod 15$

anonymous · Answer

Ah! I get it now. For some reason I forgot that the $2$ was supposed to be a power. Thanks!

kinggeorge · Answer

You're welcome.