# Congruences, Primitive Roots, Indices and Table of Indices

6. Let g be a primitive root of m. An index of a number a to the base (written ing a) is a number + such that g+≡a(mod m). Given that g is a primitive root modulo m, prove the following...

7. Construct a table of indices of all integers from....

8. Solve the congruence 9x≡11(mod 17) using the table in 7.

9. Suppose g is a primitive root modulo P (a prime) and m|p-1 (1<m<p-1). How many integral solutions are there of the congruence x^m - g ≡ (mod p) ?

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#### Solution Summary

Congruences, Primitive Roots, Indices and Table of Indices are investigated. The solution is detailed and well presented.

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