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Number Theory

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

Brocard's problem asks to find the values of n for which n!+1 is a square number m^2, where n! is the factorial (Brocard 1876, 1885). The only known solutions are n=4, 5, and ...

A modified Miller's primality test which gives a guarantee of primality or compositeness. The algorithm's running time for a number n has been proved to be as ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

A subset is a portion of a set. B is a subset of A (written B subset= A) iff every member of B is a member of A. If B is a proper subset of A (i.e., a subset other than the ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

The number 2^(1/3)=RadicalBox[2, 3] (the cube root of 2) which is to be constructed in the cube duplication problem. This number is not a Euclidean number although it is an ...

There are several different kinds of magic numbers. The digital root and magic constant are sometimes known as magic numbers. In baseball, the magic number for a team in ...