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A recursively enumerable set A is creative if its complement is productive. Creative sets are not recursive. The property of creativeness coincides with completeness. Namely, ...

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...

The plane figure formed by a sequence of circles C_1, C_2, C_3, ... that are all tangent to each other at the same point and such that the sequence of radii converges to ...

The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

The operating of shifting the leading digits of an addition into the next column to the left when the sum of that column exceeds a single digit (i.e., 9 in base 10).

If the period of a repeating decimal for a/p, where p is prime and a/p is a reduced fraction, has an even number of digits, then dividing the repeating portion into halves ...

A negative number multiplied by another negative number gives a positive number.

Reverse Polish notation (RPN) is a method for representing expressions in which the operator symbol is placed after the arguments being operated on. Polish notation, in which ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...