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 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: 18,594 Thanks: 1492 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: 1,763 Thanks: 905 Euler's Theorem if $n$ and $a$ are co-prime $a^{\phi(n)}\equiv 1 \pmod{n}$ $7$ and $45$ are co-prime $\phi(45)=24$ $7^{48} = 7^{24\cdot 2} = (7^{24})^2$ you finish

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