Pólya conjecture

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In 1919, the Hungarian mathematician Georg Pólya made the following empirische Betrachtung (empirical observation)[1]:

[D]ie Anzahl derjenigen unter den Zahlen 1,2,3,…,n, die eine gerade Anzahl von Primfaktoren haben, ist nicht größer als die Anzahl derjenigen, die eine ungerade Anzahl haben (für n≧2).
The quantity of numbers 1,2,3,…,n, having a even number of prime factors is not bigger than the quantity of those having an odd number (for n≧2).

This statement is known as the Pólya conjecture.

Footnotes

  1. "Verschiedene Bemerkungen zur Zahlentheorie." by 'Georg Pólya' (1919).