Find a primitive root modulo 101. What integers mod 101 are 5th powers? 7th powers?(adsbygoogle = window.adsbygoogle || []).push({});

-I tested 2.

-2 and 5 are the prime factors dividing phi(101)=100 so i calculated 2^50 is not congruent to 1 mod 101 and 2^20 is not congruent to 1 mod 101.

-Therefore 2 is a primitive root modulo 101

I guess this means to find find all m such that there exists x such that

x^5 = m (mod 101)

If this is the case, then how do I find these solutions?

I found that the congruence x^5 = 1 (mod 101) has gcd(5,100)=5 solutions. I also know that 2^100 = 1 (mod 101) so that ((2^20)^5) = 1 (mod 101).

I don't know where to go from there.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Number theory: primitive roots

**Physics Forums | Science Articles, Homework Help, Discussion**