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Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

A map projection which is a conformal mapping, i.e., one for which local (infinitesimal) angles on a sphere are mapped to the same angles in the projection. On maps of an ...

The equation x^p=1, where solutions zeta_k=e^(2piik/p) are the roots of unity sometimes called de Moivre numbers. Gauss showed that the cyclotomic equation can be reduced to ...

Gaussian brackets are notation published by Gauss in Disquisitiones Arithmeticae and defined by [ ]=1 (1) [a_1]=a_1 (2) [a_1,a_2]=[a_1]a_2+[ ] (3) ...

Given a series of positive terms u_i and a sequence of finite positive constants a_i, let rho=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)). 1. If rho>0, the series converges. ...

The Sendov conjecture, proposed by Blagovest Sendov circa 1958, that for a polynomial f(z)=(z-r_1)(z-r_2)...(z-r_n) with n>=2 and each root r_k located inside the closed unit ...

Five or six Wolf prizes are awarded yearly to outstanding living scientists and artists for achievements in the interest of mankind and friendly relations among peoples. In ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

Given an arithmetic progression of terms an+b, for n=1, 2, ..., the series contains an infinite number of primes if a and b are relatively prime, i.e., (a,b)=1. This result ...

A curious approximation to the Feigenbaum constant delta is given by pi+tan^(-1)(e^pi)=4.669201932..., (1) where e^pi is Gelfond's constant, which is good to 6 digits to the ...