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

Work out the order of the following elements;

[itex]33 \in Z_{36}[/itex]

3. The attempt at a solution

It's probably really simple. But this only happens when an integer times 33 is divisible by 36.

That is;

[itex] 33n = 36m [/itex]

Which I can re-arrange to find

[itex] n = 36m/33 [/itex]

Now, I can keep adding 36/33 in my calculator until I get an integer result, but surely there is an easier way? For example;

[itex] 33 \equiv -3mod36 [/itex]

Which suggests that 36/3 = 12 is the order of 33. This is fine and dandy, but what happens when I get to a question like, find the order of

[itex]15 \in Z_{36}[/itex]

Then

[itex] 15 \equiv -21mod36 [/itex]

Which means I'm back to the same problem again. My modular arithmetic is fairly poor, so how would I work this out?

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# Homework Help: When is m33 divisible by 36? (m is an integer).

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