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Closed form solution of x^2 = 2 mod Fermat number
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2005-09-28, 17:53
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Yamato
Sep 2005
Berlin
2×3×11 Posts
Let F(n) = 2^(2^n) + 1.
Then the "trivial" square root of 2 is
sqrt(2) = F(n-1) * inv(F(n-2) - 1) (mod F(n))
(inv is the inverse number mod F(n))
because of the real factorization
F(n) = F(n-1)^2 - x^2
where x = (F(n-2) - 1)*sqrt(2)
Yamato
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