Page 1 of 1
= X р = р 4. Let p be prime. Prove that, if d e Z satisfies gcd(d, p - 1) = 1, then the function f:FX + F defined by f(a
Posted: Thu May 12, 2022 4:12 pm
by answerhappygod
- 1 (56.26 KiB) Viewed 60 times
= X р = р 4. Let p be prime. Prove that, if d e Z satisfies gcd(d, p - 1) = 1, then the function f:FX + F defined by f(a) = ad is bijective. (Hint: The integer d admits an inverse modulo p 1 by Problem 3. Use this inverse to construct an inverse function for f. Note that you cannot prove injectivity by "taking d-th roots,” as this assumes that d-th roots are unique, which is equivalent to the statement you need to prove.)