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The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy ...

The imaginary number i=sqrt(-1), i.e., the square root of -1. The imaginary unit is denoted and commonly referred to as "i." Although there are two possible square roots of ...

The operation of taking an nth root of a number.

A root having multiplicity n=1 is called a simple root. For example, f(z)=(z-1)(z-2) has a simple root at z_0=1, but g=(z-1)^2 has a root of multiplicity 2 at z_0=1, which is ...

A simple root of a Lie algebra is a positive root that is not the sum of two positive roots.

Trigonometric functions of npi/11 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 11 is not a ...

Trigonometric functions of npi/13 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 13 is not a ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...