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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, [ 1 ] and proved false in 1958 by C. Brian Haselgrove .
Polya begins Volume I with a discussion on induction, not mathematical induction, but as a way of guessing new results.He shows how the chance observations of a few results of the form 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, etc., may prompt a sharp mind to formulate the conjecture that every even number greater than 4 can be represented as the sum of two odd prime numbers.
Conjecture Field Comments Eponym(s) Cites 1/3–2/3 conjecture: order theory: n/a: 70 abc conjecture: number theory: ⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé. [1] Proof claimed in 2012 by Shinichi Mochizuki: n/a ...
Riemann's original use of the explicit formula was to give an exact formula for the number of primes less than a given number. To do this, take F(log(y)) to be y 1/2 /log(y) for 0 ≤ y ≤ x and 0 elsewhere. Then the main term of the sum on the right is the number of primes less than x.
The earliest published statement of the conjecture seems to be in Montgomery (1973). [1] [2] David Hilbert did not work in the central areas of analytic number theory, but his name has become known for the Hilbert–Pólya conjecture due to a story told by Ernst Hellinger, a student of Hilbert, to André Weil. Hellinger said that Hilbert ...
Colin Brian Haselgrove (26 September 1926 – 27 May 1964) was an English mathematician who is best known for his disproof of the Pólya conjecture in 1958. [1] Haselgrove was educated at Blundell's School and from there won a scholarship to King's College, Cambridge. He obtained his Ph.D., which was supervised by Albert Ingham, from Cambridge ...
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What I need is a formula or algorithm for determining the number of servers needed to meet a given QoS target, which is of the form: (wait time + service time) ≤ T, for ≥ X% of customers, for some given T and X. Thanks in advance. --173.49.19.4 05:37, 10 February 2015 (UTC)