February 21st, 2017, 05:48 PM  #1 
Newbie Joined: Feb 2017 From: LA Posts: 2 Thanks: 0  Euler's Theorum
Compute ø (45); Compute 7^48 mod 45 using Euler’s Theorem

February 21st, 2017, 07:04 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326 
What progress have you made so far?

February 21st, 2017, 08:18 PM  #3 
Newbie Joined: Feb 2017 From: LA Posts: 2 Thanks: 0 
a = 7 n = 45 phi n = 24 gcd (7, 45) = 1 7^24 = 1 mod 24 not sure what to do. Last edited by qwaz; February 21st, 2017 at 08:20 PM. 
February 21st, 2017, 08:26 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,638 Thanks: 1475 
Euler's Theorem if $n$ and $a$ are coprime $a^{\phi(n)}\equiv 1 \pmod{n}$ $7$ and $45$ are coprime $\phi(45)=24$ $7^{48} = 7^{24\cdot 2} = (7^{24})^2$ you finish 

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