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= 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
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= 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
= 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.)
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