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If p is a prime number and a is a natural number, then a^p=a (mod p). (1) Furthermore, if pa (p does not divide a), then there exists some smallest exponent d such that ...

An Abelian integral, are also called a hyperelliptic integral, is an integral of the form int_0^x(dt)/(sqrt(R(t))), where R(t) is a polynomial of degree >4.

A sequence of random variates X_0, X_1, ... is called absolutely fair if for n=1, 2, ..., <X_1>=0 and <X_(n+1)|X_1,...,X_n>=0 (Feller 1971, p. 210).

A theory which satisfies all the Eilenberg-Steenrod axioms with the possible exception of the long exact sequence of a pair axiom, as well as a certain additional continuity ...

Given a property P, if P(x)∼x as x->infty (so, using asymptotic notation, the number of numbers less than x not satisfying the property P is o(x), where o(x) is one of the ...

A solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...

The function psi(x)={sin(x/c) |x|<cpi; 0 |x|>cpi, (1) which occurs in estimation theory.

A hyperbolic linear map R^n->R^n with integer entries in the transformation matrix and determinant +/-1 is an Anosov diffeomorphism of the n-torus, called an Anosov ...

An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle. An example from physics is the Bethe Ansatz (Müller).

The BCH code is an error-correcting code that is a generalization of the Reed-Muller error-correcting code used by the Voyager 2 spacecraft.