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Let X_1 and X_2 be the number of successes in variates taken from two populations. Define p^^_1 = (x_1)/(n_1) (1) p^^_2 = (x_2)/(n_2). (2) The estimator of the difference is ...

Find two numbers such that x^2=y^2 (mod n). If you know the greatest common divisor of n and x-y, there exists a high probability of determining a prime factor. Taking small ...

A prismatoid having planar sides and the same number of vertices in both of its parallel planes. The faces of a prismoid are therefore either trapezoids or parallelograms. ...

A proper subgroup is a proper subset H of group elements of a group G that satisfies the four group requirements. "H is a proper subgroup of G" is written H subset G. The ...

A proper subset S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is ...

For N=k·2^n+1 with k odd and 2^n>k, if there exists an integer a such that a^((N-1)/2)=-1 (mod N), then N is prime. A prime of this form is known as a Proth prime.

A scalar which reverses sign under inversion is called a pseudoscalar. For example, the scalar triple product A·(BxC) is a pseudoscalar since A·(BxC)=-[-A·((-B)x(-C))].

Pythagoras's constant sqrt(2) has decimal expansion sqrt(2)=1.4142135623... (OEIS A000129), It was computed to 2000000000050 decimal digits by A. J. Yee on Feb. 9, 2012. The ...

A plane figure consisting of four points, each of which is joined to two other points by a line segment (where the line segments may intersect). A quadrangle may therefore be ...

To compute an integral of the form int(dx)/(a+bx+cx^2), (1) complete the square in the denominator to obtain int(dx)/(a+bx+cx^2)=1/cint(dx)/((x+b/(2c))^2+(a/c-(b^2)/(4c^2))). ...