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Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

Solomon's seal knot is the prime (5,2)-torus knot 5_1 with braid word sigma_1^5. It is also known as the cinquefoil knot (a name derived from certain herbs and shrubs of the ...

Abstract Algebra

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

An anti-analytic function is a function f satisfying the condition (df)/(dz)=0. (1) Using the result ...

Let T be an ergodic endomorphism of the probability space X and let f:X->R be a real-valued measurable function. Then for almost every x in X, we have 1/nsum_(j=1)^nf ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...

In December 1920, M. Schönfinkel presented in a report to the Mathematical Society in Göttingen a new type of formal logic based on the concept of a generalized function ...

A function, or the symbol representing a function, which corresponds to English conjunctions such as "and," "or," "not," etc. that takes one or more truth values as input and ...