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The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

A hash function H projects a value from a set with many (or even an infinite number of) members to a value from a set with a fixed number of (fewer) members. Hash functions ...

The prime spiral, also known as Ulam's spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes indicated in some way along the ...

Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...

A prime p is said to be a Sophie Germain prime if both p and 2p+1 are prime. The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, ... (OEIS ...

A Wieferich prime is a prime p which is a solution to the congruence equation 2^(p-1)=1 (mod p^2). (1) Note the similarity of this expression to the special case of Fermat's ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

The distribution function D(x), also called the cumulative distribution function (CDF) or cumulative frequency function, describes the probability that a variate X takes on a ...

The free module of rank n over a nonzero unit ring R, usually denoted R^n, is the set of all sequences {a_1,a_2,...,a_n} that can be formed by picking n (not necessarily ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...