mersenneforum.org Modular arithmetic query
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 2020-06-08, 11:43 #1 garo     Aug 2002 Termonfeckin, IE AC316 Posts Modular arithmetic query Apologies if this is very basic. Could anyone tell me why $(g^{a}\ mod\ p) \cdot (g^{b}\ mod\ p) \ mod\ p\equiv g^{(a+b)\ mod\ (p-1)}\ mod\ p$ Last fiddled with by garo on 2020-06-08 at 11:47
 2020-06-08, 11:53 #2 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 5,741 Posts
 2020-06-08, 12:07 #3 garo     Aug 2002 Termonfeckin, IE 5·19·29 Posts Right. I got that far but couldn't make the connection. How do I get from the totient function to (a+b) mod (p-1)?
2020-06-08, 12:09   #4
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

5,741 Posts

Quote:
 Originally Posted by garo Right. I got that far but couldn't make the connection. How do I get from the totient function to (a+b) mod (p-1)?
For primes the totient function is simply p-1. So multiples of p-1 in the exponent can be ignored.

 2020-06-08, 12:15 #5 garo     Aug 2002 Termonfeckin, IE 5·19·29 Posts Gotcha. Thanks for your help. Not sure why I was making it more complicated in my head. Last fiddled with by garo on 2020-06-08 at 12:16

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