What is the remainder of (16937^30)/31 ?
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Heya...
6937 & 31 are coprimes so we can use Euler's theorem to find 16937^30 mod 31.
By Euler's totient function,
Phi (31) = 30.
For a prime p, phi (p) = p-1.
By Euler's theorem,
16937^[phi (31)] mod 31 = 1.
So, 16937^30 mod 31 = 1.
6937 & 31 are coprimes so we can use Euler's theorem to find 16937^30 mod 31.
By Euler's totient function,
Phi (31) = 30.
For a prime p, phi (p) = p-1.
By Euler's theorem,
16937^[phi (31)] mod 31 = 1.
So, 16937^30 mod 31 = 1.
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