Find a primitive root modulo 89 and use the answer to find a number a so that the order of a modulo 89 is 8.

Does this mean

a^8=1 (mod 89)?

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- Oct 15th 2008, 01:48 AMRichmondPrimitive Roots
Find a primitive root modulo 89 and use the answer to find a number a so that the order of a modulo 89 is 8.

Does this mean

a^8=1 (mod 89)? - Oct 15th 2008, 05:11 PMJhevon
- Oct 15th 2008, 05:44 PMThePerfectHacker
We use the result that the primes which have as a quadradic residue are of the form . This result can be established using quadradic reciprocity. Since , a prime, does not have this form it means . Thus, by Euler's criterion. Let be order of then . But if then and it would follow that which is a contradiction. Therefore, and consequently is a primitive root of .

It follows that has order mod . - Oct 15th 2008, 07:58 PMRichmond
thank you.