The Pólya conjecture, now refuted, posited that the summatory function L(m) = sum_(n=1)^mλ(n) of the Liouville function is always nonpositive.
False
for all _(m, m element Z^+) sum_(n=1)^mλ(n)<=0
formulation date | 1919 (106 years ago) formulator | George Pólya status | refuted proof date | 1958 (39 years later) (67 years ago) prover | C. Brian Haselgrove
sum_(n=1)^mλ(n)<=0
The smallest counterexample is known to occur at m = 906150257.
