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Given a number n, Fermat's factorization methods look for integers x and y such that n=x^2-y^2. Then n=(x-y)(x+y) (1) and n is factored. A modified form of this observation ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

The Golay code is a perfect linear error-correcting code. There are two essentially distinct versions of the Golay code: a binary version and a ternary version. The binary ...

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...

The appearance of nontrivial zeros (i.e., those along the critical strip with R[z]=1/2) of the Riemann zeta function zeta(z) very close together. An example is the pair of ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

The modular equation of degree n gives an algebraic connection of the form (K^'(l))/(K(l))=n(K^'(k))/(K(k)) (1) between the transcendental complete elliptic integrals of the ...

The term "pathological" is used in mathematics to refer to an example specifically cooked up to violate certain almost universally valid properties. Pathological problems ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...