- #1
joshuathefrog
- 14
- 0
Homework Statement
Find one solution (or prove no solutions exist) to the equation
x100 = 3 mod 83, where "=" means "congruent to"
Homework Equations
Possibly Fermat's theorem: If p is prime and p does not divide a, then ap-1 = 1 mod p.
The Attempt at a Solution
83 is prime. I know that 101 is prime, and so ap-1 == x^100 if p == 101. However, not sure how to deal with the mod 83 then.
Alternatively, using p == 83, then x82 = 1 mod 83, but this doesn't seem to help much either.
Any suggestions?