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February 21st, 2017, 04:48 PM   #1
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Euler's Theorum

Compute ø (45); Compute 7^48 mod 45 using Euler’s Theorem
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February 21st, 2017, 06:04 PM   #2
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February 21st, 2017, 07:18 PM   #3
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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 07:20 PM.
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February 21st, 2017, 07:26 PM   #4
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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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