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Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies d=1 (mod 4) or d=8,12 (mod 16). The function ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

The Frobenius equation is the Diophantine equation a_1x_1+a_2x_2+...+a_nx_n=b, where the a_i are positive integers, b is an integer, and the solutions x_i are nonnegative ...

The least common denominator of a collection of fractions (p_1)/(q_1),...,(p_n)/(q_n) is the least common multiple LCM(q_1,...,q_n) of their denominators.

kappa(d)={(2lneta(d))/(sqrt(d)) for d>0; (2pi)/(w(d)sqrt(|d|)) for d<0, (1) where eta(d) is the fundamental unit and w(d) is the number of substitutions which leave the ...

The Diophantine equation x_1^2+x_2^2+...+x_n^2=ax_1x_2...x_n which has no integer solutions for a>n.

Suppose that {f_n} is a sequence of measurable functions, that f_n->f pointwise almost everywhere as n->infty, and that |f_n|<=g for all n, where g is integrable. Then f is ...

The maximum degree, sometimes simply called the maximum degree, of a graph G is the largest vertex degree of G, denoted Delta.

Obstruction theory studies the extensibility of maps using algebraic gadgets. While the terminology rapidly becomes technical and convoluted (as Iyanaga and Kawada (1980) ...