Solve $x^{83}\equiv 7\pmod {139}$
Solve the congruence $x^{83}\equiv 7\pmod {139}$.
Please explain your working at each stage as if you were teaching an undergraduate student who were learning this for the first time! I am really trying to learn how to solve these type of. Qs. I notice that both the mod and exponent are prime. I suspect that you might need to use a primitive root, and would appreciate extra insights/explanations of alternative approaches or methods. Ideally, I would like to learn the most efficient methods possible.

133
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

4.8K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 522 views
- $50.00
Related Questions
- Wierdly Rational Fractions
- Elementary num theory Q: or
- Prove the following limits of a sequence of sets?
- Solve $abc=2(a-2)(b-2)(c-2)$ where $a,b $ and $c$ are integers
- Quadratic residue
- Why even/odd coordinates correspond to positive/negative signs in elliptic curves
- Elementary group theory and number theory questions involving prime numbers, permutation groups and dihedral groups. Introduction to number theory questions
- Prove that $p^2-1$ is divisible by 24 for any prime number $p > 3$.