[madhapper]

Let p be a prime. Prove that if a is an element of Z*_p then a^(p-1) = 1, i.e. for any integer a not divisible by p, a^p-1 is equivalent to 1 (mod p)

find 2^183 (mod37)

[RichE]

(Original post by madhapper)
Let p be a prime. Prove that if a is an element of Z*_p then a^(p-1) = 1, i.e. for any integer a not divisible by p, a^p-1 is equivalent to 1 (mod p)

find 2^183 (mod37)

From FLT 2^36 = 1 mod 37.

So 2^183 = 2^180 * 2^3 = (2^36)^5 * 2^3 = 1^5 * 2^3 = 8 (mod 37)

[dvs]

The proof is available on many websites. Just do a quick google search.

2^36 = 1 (mod 37) and 36*5=180, then:
2^183 = 2^(180) . 2^3 = 2^(36)^5 . 2^3 = 1^5 . 2^3 = 8 (mod 37)

[dvs]

I have to start posting faster...