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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 (106 years ago)
formulator | George Pólya
status | refuted
proof date | 1958 (39 years later) (67 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.

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