(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all elements of Z^{*}_{19}of multiplicative order 18.

2. Relevant equations

a^{k}[tex]\equiv[/tex]1 (mod n)

3. The attempt at a solution

So for a [tex]\in[/tex] Z^{*}_{19}to have the multiplicative order 18 we have to satisfy the equivalence a^{18}[tex]\equiv[/tex] 1(mod 19), but the has to be a "smarter" way of calculating "a" than by just plug and chug numbers 1 through 18 to find the set thats equivalent to 1(mod 19)

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# Homework Help: Multiplicative Order

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