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  I am still confused of how we can expect the order of an modulo multiplication group
 
  I am still confused of how we can expect the order of an modulo multiplication group
 
  which has very big orders without arranging each element one by one.
 
  which has very big orders without arranging each element one by one.
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I assume you are referring to finding the order of <math>U(750)</math>.  Here is how I did it on the homework last week:
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Find a formula for <math>|U(p^n)|</math> where p is a prime.  Then, try factoring 750 into two numbers, one of them in a convenient form.  You can get <math>750 = 6*5^3</math>.  Five is prime, and we know <math>|U(5^3)|</math>.  We can also get <math>|U(6)|</math> pretty easily.  Then, from the previous homework, we had a conjecture on what, in general, is <math>|U(a*b)|</math>.  Use that conjecture with the factors of 750 you generated, and there's your prediction.  Of course, if you proved your conjecture, it would cease to be simply a prediction.
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-Josh Magner

Revision as of 14:08, 28 September 2008

I am still confused of how we can expect the order of an modulo multiplication group
which has very big orders without arranging each element one by one.

I assume you are referring to finding the order of $ U(750) $. Here is how I did it on the homework last week: Find a formula for $ |U(p^n)| $ where p is a prime. Then, try factoring 750 into two numbers, one of them in a convenient form. You can get $ 750 = 6*5^3 $. Five is prime, and we know $ |U(5^3)| $. We can also get $ |U(6)| $ pretty easily. Then, from the previous homework, we had a conjecture on what, in general, is $ |U(a*b)| $. Use that conjecture with the factors of 750 you generated, and there's your prediction. Of course, if you proved your conjecture, it would cease to be simply a prediction. -Josh Magner

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