×

# 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, 4 months ago

Sort by:

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. · 3 years, 4 months ago