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Bertrand’s postulate over the Gaussian integers is an extension of the idea of the distribution of primes, but in this case on the complex plane. Thus, as Gaussian primes extend over the plane and not only along a line, and doubling a complex number is not simply multiplying by 2 but doubling its norm (multiplying by 1+i), different ...
In mathematics, Bertrand's postulate (now a theorem) states that, for each , there is a prime such that < <.First conjectured in 1845 by Joseph Bertrand, [1] it was first proven by Chebyshev, and a shorter but also advanced proof was given by Ramanujan.
Copeland and Erdős's proof that their constant is normal relies only on the fact that is strictly increasing and = + (), where is the n th prime number. More generally, if is any strictly increasing sequence of natural numbers such that = + and is any natural number greater than or equal to 2, then the constant obtained by concatenating "0."
Proof of Bertrand's postulate; Fermat's theorem on sums of two squares; Two proofs of the Law of quadratic reciprocity; Proof of Wedderburn's little theorem asserting that every finite division ring is a field; Four proofs of the Basel problem; Proof that e is irrational (also showing the irrationality of certain related numbers) Hilbert's ...
Daniel Larsen (born 2003) is an American mathematician known for proving [1] a 1994 conjecture of W. R. Alford, Andrew Granville and Carl Pomerance on the distribution of Carmichael numbers, commonly known as Bertrand's postulate for Carmichael numbers. [2]
Illustration for a proof of the Erdős–Anning theorem. Given three non-collinear points A, B, C with integer distances from each other (here, the vertices of a 3–4–5 right triangle), the points whose distances to A and B differ by an integer lie on a system of hyperbolas and degenerate hyperbolas (blue), and symmetrically the points whose distances to B and C differ by an integer lie on ...
Joseph Louis François Bertrand (French pronunciation: [ʒozɛf lwi fʁɑ̃swa bɛʁtʁɑ̃]; 11 March 1822 – 5 April 1900) was a French mathematician whose work emphasized number theory, differential geometry, probability theory, economics and thermodynamics.
Bertrand, an 1865 steamboat that sank in the Missouri River; Bertrand Baudelaire, a fictional character in A Series of Unfortunate Events; Bertrand competition, an economic model where firms compete on price; Bertrand's theorem, a theorem in classical mechanics; Bertrand's postulate, a theorem about the distribution of prime numbers