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What is the remainder when (3^18132 )is divided by 17?
The answer is 13.
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1 solution
cant it be done without coding????
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Yes, with Euler's Theorem. 3 and 17 are coprime so it can be applied.
ϕ ( 1 7 ) = 1 6 , because 17 is a prime number.
3 1 8 1 3 2 = 3 1 6 ⋅ 1 1 3 3 + 4 = ( 3 1 6 ) 1 1 3 3 3 4 ≡ 3 4 ( m o d 1 7 )
And now 3 4 ≡ 1 3 ( m o d 1 7 )
Python code:
(3**18132)%17