4. How many primitive roots does 98 have? Find all of them. (That is, find one primitive root g, and then determine all exponents k such that the least residue of g^k is also a primitive root.)
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The number of primitive roots of a number n is given by the Euler's totient function φ(φ(n)). First, we need to find φ(98). 98 = 2 * 7^2. So, φ(98) = 98 * (1 - 1/2) * (1 - 1/7) = 42. Now, we need to find φ(42). 42 = 2 * 3 * 7. So, φ(42) = 42 * (1 - Show more…
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How many primitive roots does 98 have? Find all of them. (That is, find one primitive root g, and then determine all exponents k such that the least residue of g^k is also a primitive root.)
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