(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find one solution (or prove no solutions exist) to the equation

x^{100}= 3 mod 83, where "=" means "congruent to"

2. Relevant equations

Possibly Fermat's theorem: If p is prime and p does not divide a, then a^{p-1}= 1 mod p.

3. The attempt at a solution

83 is prime. I know that 101 is prime, and so a^{p-1}== x^^{100}if p == 101. However, not sure how to deal with the mod 83 then.

Alternatively, using p == 83, then x^{82}= 1 mod 83, but this doesn't seem to help much either.

Any suggestions?

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

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!

# Homework Help: Solving a polynomial congruence?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

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