Riemann Hypothesis
zeta(s) = 0 => Re(s) = 1/2
Proof:
zeta(s) = 0
= SUM(n=1 to 99999…) n**-s
= SUM(n=1 to 99999…) n**-s.n**(2s-1) [0<=Re(s)<1 => 2Re(s)-1<1]
= SUM(n=1 to 99999…) n**(s-1)
= zeta(1-s)
Therefore, Re(1-s)=Re(s), [because f(x) = f(y) over a range => x = y]
i.e. Re(s) =1/2