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The idea for the general proof follows the above supplemental case: Find an algebraic integer that somehow encodes the Legendre symbols for p, then find a relationship between Legendre symbols by computing the qth power of this algebraic integer modulo q in two different ways, one using Euler's criterion the other using the binomial theorem.
De Bruijn–Erdős theorem (incidence geometry) De Bruijn–Erdős theorem (graph theory) De Finetti's theorem (probability) De Franchis theorem (Riemann surfaces) De Gua's theorem ; De Moivre's theorem (complex analysis) De Rham's theorem (differential topology) Deduction theorem ; Dehn-Nielsen-Baer theorem (geometric topology)
Mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. This notation consists of symbols used for representing operations, unspecified numbers, relations and any other mathematical objects, and then assembling them into expressions and ...
The Chinese remainder theorem appears as an exercise [16] in Sunzi Suanjing (between the third and fifth centuries). [17] (There is one important step glossed over in Sunzi's solution: [note 4] it is the problem that was later solved by Āryabhaṭa's Kuṭṭaka – see below.)
In the geometry of numbers, the subspace theorem was obtained by Wolfgang M. Schmidt in 1972. [6] It states that if n is a positive integer, and L 1,...,L n are linearly independent linear forms in n variables with algebraic coefficients and if ε>0 is any given real number, then the non-zero integer points x in n coordinates with
This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient. Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend; for example, 10 / 3 leaves a remainder of 1, as 10 is not a multiple of 3.