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Roth's theorem on arithmetic progressions. Roth's theorem on arithmetic progressions is a result in additive combinatorics concerning the existence of arithmetic progressions in subsets of the natural numbers. It was first proven by Klaus Roth in 1953. [1] Roth's theorem is a special case of Szemerédi's theorem for the case .
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The cube function is the function x ↦ x 3 (often denoted y = x 3) that maps a number to its cube. It is an odd function, as (−n) 3 = −(n 3). The volume of a geometric cube is the cube of its side length, giving rise to the name. The inverse operation that consists of finding a number whose cube is n is called extracting the cube root of n ...
The Descartes Systems Group Inc. (commonly referred to as Descartes) is a Canadian multinational technology company specializing in logistics software, supply chain management software, and cloud -based services for logistics businesses. Descartes is perhaps best known for its abrupt and unexpected turnaround in the mid-2000s after coming close ...
Adjoining a root of x 3 + x 2 − 2x − 1 to Q yields a cyclic cubic field, and hence a totally real cubic field. It has the smallest discriminant of all totally real cubic fields, namely 49. The field obtained by adjoining to Q a root of x 3 + x 2 − 3x − 1 is an example of a totally real cubic field that is not cyclic. Its discriminant is ...
Cube root law; This page is a redirect. The following categories are used to track and monitor this redirect: From a page move: This is a redirect from a page that ...
The cube rule or cube law is an empirical observation regarding elections under the first-past-the-post system. The rule suggests that the party getting the most votes is over-represented (and conversely, the party getting the fewest votes is under-represented). It was first formulated in a report on British elections in 1909, then extended to ...
Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.