Hi all, just wondering what the method is to find an integer with order t mod m.

For example, find all integers that have order 11 (mod 45).

I know you can geuss and test, but I'm thinking there must be a faster way.

Thanks.

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- Mar 18th 2010, 02:55 PMseven.jMultiplicative Order
Hi all, just wondering what the method is to find an integer with order t mod m.

For example, find all integers that have order 11 (mod 45).

I know you can geuss and test, but I'm thinking there must be a faster way.

Thanks. - Mar 18th 2010, 03:22 PMchiph588@
- Mar 18th 2010, 03:30 PMchiph588@
- Mar 18th 2010, 03:42 PMchiph588@
One last thing:

If is a primitive root, then we know that i.e. for some .

So all one has to do to find for any , is find and use the formula .

In summary, knowing the order of a primitive root gives you the order of every number in your group.