Get Math Help

GET TUTORING NEAR ME!

(800) 434-2582

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    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.

    Classes

    refuted conjectures | solved mathematics problems

    Back to List | POWERED BY THE WOLFRAM LANGUAGE