On Wednesday, 26 June 2013 at 23:14:09 UTC, H. S. Teoh wrote:
I think the 4-cycle algorithm is probably still the best one I've seen.
All (correct) mathematically based answers are 4-cycle.
begin very sloppy proof with mixed up notation:
Let f^2(x) = -x
f^4(x) = f^2(f^2(x))
= f^2(-x)
= -(-x)
= x
Therefore:
f^4 = 1
f^{4n} = 1^n = 1, n in N
<==> f^{4n}(x) = x
□
