remainder of the product of the relatively prime numbersby whodsow Tags: congruence, euler's formula 

#1
May2809, 07:28 AM

P: 12

Hi all, I had a problem, pls help me.
Let [tex]b_1 < b_2 < \cdots < b_{\varphi(m)}[/tex] be the integers between 1 and m that are relatively prime to m (including 1), of course, [tex]\varphi(m)[/tex] is the number of integers between 1 and m that are relatively prime to m, and let [tex]B = b_1b_2b_3{\cdots}b_{\varphi(m)}[/tex] be their product. Please find a pattern for when [tex]B\equiv1 ({\bmod}\ m)[/tex] and when [tex]B\equiv1 ({\bmod}\ m)[/tex]. Thanks and Regards. 



#2
May2809, 08:57 AM

Sci Advisor
HW Helper
P: 3,680





#3
May2909, 09:52 AM

P: 12

Thank you, I've gotten the similar table.




#4
May2909, 10:52 AM

P: 12

remainder of the product of the relatively prime numbers
Media Man told me it is a generalization of Wilson's Theorem(http://mathworld.wolfram.com/WilsonsTheorem.html)
Thanks. 


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