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Pólya Conjecture
Statement
The Pólya conjecture, now refuted, posited that the summatory function L(m) = sum_(n=1)^mλ(n) of the Liouville function is always nonpositive.
Solution
False
Formal statement
for all _(m, m element Z^+) sum_(n=1)^mλ(n)<=0
History
formulation date | 1919 (107 years ago) formulator | George Pólya status | refuted proof date | 1958 (39 years later) (68 years ago) prover | C. Brian Haselgrove
Associated equation
sum_(n=1)^mλ(n)<=0
Current evidence
The smallest counterexample is known to occur at m = 906150257.