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The ultraradical symbol is a notation thet can be used to express solutions not obtainable by finite root extraction. The solution to the irreducible quintic equation x^5+x=a ...

The point of concurrence of the six planes in Monge's tetrahedron theorem.

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

If (1-z)^(a+b-c)_2F_1(2a,2b;2c;z)=sum_(n=0)^inftya_nz^n, then where (a)_n is a Pochhammer symbol and _2F_1(a,b;c;z) is a hypergeometric function.

Let R be a ring, let A be a subring, and let B be an ideal of R. Then A+B={a+b:a in A,b in B} is a subring of R, A intersection B is an ideal of A and (A+B)/B=A/(A ...

Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and (R/I)/(J/I)=R/J.

Let f(z) be an analytic function in |z-a|<R. Then f(z)=1/(2pi)int_0^(2pi)f(z+re^(itheta))dtheta for 0<r<R.