Question

78.Show that 3 is a primitive root modulo 17. How many primitive roots does 17 have? Find them. 79.Is the congruence x^12 ? 16 mod 17 solvable? If yes, find its solutions. Hint: Use question #78.

          78.Show that 3 is a primitive root modulo 17. How many primitive roots does 17
have? Find them.
79.Is the congruence x^12 ? 16 mod 17 solvable? If yes, find its solutions. Hint: Use
question #78.

Added by Jennifer D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/19/2023

Step 1

A primitive root modulo 17 is an integer g such that the powers of g generate all the non-zero residues modulo 17. In other words, the set $\{g^1, g^2, \dots, g^{16}\}$ should contain all the integers from 1 to 16 modulo 17. Since 17 is a prime number, we know Show more…

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78. Show that 3 is a primitive root modulo 17. How many primitive roots does 17 have? Find them. 79. Is the congruence x^12 = 16 mod 17 solvable? If yes, find its solutions. Hint: Use question #78.