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• Obvious typo in the statement of my theorem is corrected here. If P is the product of two primes, x and y, P = x y, then for any relatively prime integer b, to
Message 1 of 1 , Jun 23, 2012
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Obvious typo in the statement of my theorem is corrected here.

If P is the product of two primes, x and y,

P = x y,

then
for any relatively prime integer b, to P,

b^(P+1) = b^(x+y) mod P.

Proof:

The number of positive integers< P that are
relatively prime to P is (x-1)(y-1).

By fundamental group theory theorem,
for any relatively prime integer b, to P,

b^( (x-1)(y-1)) = 1 mod P.

b^(x y - y - x + 1) = 1 mod P.

b^(x y + 1 - (x+y) ) = 1 mod p

b^(x y + 1) = b^(x+y) mod P

b^(P + 1) = b^(x+y) mod P.

Kermit
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