[mpenguin]

Originally Posted by Yamato

Let F(n) = 2^(2^n) + 1.

Then the "trivial" square root of 2 is

Yes, the square root of 2 is trivial mod Fn.

(2+2^(1/2))^2 and (2+(2+2^(1/2))^(1/2))^(1/2) mod Fn are a little more subtle.