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In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

Mills (1947) proved the existence of a real constant A such that |_A^(3^n)_| (1) is prime for all integers n>=1, where |_x_| is the floor function. Mills (1947) did not, ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...

The smallest value of a set, function, etc. The minimum value of a set of elements A={a_i}_(i=1)^N is denoted minA or min_(i)a_i, and is equal to the first element of a ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

The modified bessel function of the second kind is the function K_n(x) which is one of the solutions to the modified Bessel differential equation. The modified Bessel ...

By way of analogy with the prime counting function pi(x), the notation pi_(a,b)(x) denotes the number of primes of the form ak+b less than or equal to x (Shanks 1993, pp. ...

The transformation of a sequence a_1, a_2, ... with a_n=sum_(d|n)b_d (1) into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n=sum_(d|n)mu(n/d)a_d. (2) The ...

The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is ...