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A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

The function [x] which gives the smallest integer >=x, shown as the thick curve in the above plot. Schroeder (1991) calls the ceiling function symbols the "gallows" because ...

An algorithm for making tables of primes. Sequentially write down the integers from 2 to the highest number n you wish to include in the table. Cross out all numbers >2 which ...

A polygonal number and 6-polygonal number of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... (OEIS A000384). The generating function for the hexagonal numbers is ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

L_nu(z) = (1/2z)^(nu+1)sum_(k=0)^(infty)((1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)) (1) = (2(1/2z)^nu)/(sqrt(pi)Gamma(nu+1/2))int_0^(pi/2)sinh(zcostheta)sin^(2nu)thetadtheta, ...

A Sierpiński number of the second kind is a number k satisfying Sierpiński's composite number theorem, i.e., a Proth number k such that k·2^n+1 is composite for every n>=1. ...

If a prime number divides a norm but not the bases of the norm, it is itself a norm.

A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.