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.
Follow Math Help Forum on Facebook and Google+
Originally Posted by seven.j 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. Well for starters, the order always divides . Here, and so no number exists with order modulo .
Originally Posted by seven.j 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. Also, if , then the order of divides .
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.
View Tag Cloud