Waste less time on Facebook — follow Brilliant.
×

A residue a is called a generator modulo prime p if every non-zero residue modulo p equals some power of a modulo p.

please dont give the answer just give me some examples to understand generator modulo prime

Note by Superman Son
3 years, 9 months ago

No vote yet
4 votes

Comments

Sort by:

Top Newest

Here's an example: 3 is a generator mod 7 since

\(3^0 \equiv 1 \pmod 7,\ 3^1 \equiv 3\pmod 7,\ 3^2 \equiv 2\pmod 7,\) \(3^3 \equiv 6 \pmod 7,\ 3^4 \equiv 4\pmod 7,\ 3^5 \equiv 5\pmod 7.\)

So all the non-zero elements mod 7 (namely 1-6) can be expressed as a power of 3.

On the other hand, 2 is not a generator mod 7 since its powers are 1, 2 and 4 mod 7. C Lim · 3 years, 9 months ago

Log in to reply

@C Lim thank you very much i got it(got the problem).couldnt do without your help Superman Son · 3 years, 9 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...