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Pólya conjecture

In number theory, the Pólya conjecture (or Pólya's conjecture) stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was set forth by the Hungarian mathematician George Pólya in 1919, and proven false in 1958 by C. Brian Haselgrove. Though mathematicians typically…

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Statement

Natural numbersLiouville function
2 related topics

Disproof

R. Sherman Lehman
1 related topics

Overview

Number theoryNatural numbersLess thanPrime factorsConjecture
10 related topics

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Overview

Statement

Disproof

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Pólya conjecture

Nodes17
Edges16
Triples12
Avg. degree1.88
Density0.117647
Components1

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Pólya conjecture

Top relations

related to Disproof · 5
Pólya conjecture → Brian Haselgrove, He, Minoru Tanaka, Sherman Lehman, The Pólya
related to Statement · 4
Pólya conjecture → Equivalently, Liouville, Repeated, The Pólya
related to External links · 3
Pólya conjecture → Eric, MathWorld, Weisstein

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Important terminology

conjecture pólya number prime factors numbers counterexample displaystyle odd set 906 showed pólya's true statement even stated natural less given

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Pólya conjecturerelated to DisproofThe Pólya0.60section
Pólya conjecturerelated to DisproofBrian Haselgrove0.60section
Pólya conjecturerelated to DisproofHe0.60section
Pólya conjecturerelated to DisproofSherman Lehman0.60section
Pólya conjecturerelated to DisproofMinoru Tanaka0.60section
Pólya conjecturerelated to External linksWeisstein0.60section
Pólya conjecturerelated to External linksEric0.60section
Pólya conjecturerelated to External linksMathWorld0.60section
Pólya conjecturerelated to StatementThe Pólya0.60section
Pólya conjecturerelated to StatementRepeated0.60section
Pólya conjecturerelated to StatementEquivalently0.60section
Pólya conjecturerelated to StatementLiouville0.60section

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