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The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the ...

Let K be a number field with r_1 real embeddings and 2r_2 imaginary embeddings and let r=r_1+r_2-1. Then the multiplicative group of units U_K of K has the form ...

If alpha is any number and m and n are integers, then there is a rational number m/n for which |alpha-m/n|<=1/n. (1) If alpha is irrational and k is any whole number, there ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

A set partition of a set S is a collection of disjoint subsets of S whose union is S. The number of partitions of the set {k}_(k=1)^n is called a Bell number.

The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines. A connection between automata theory ...

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

The fifth of Peano's axioms, which states: If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

The number sign # sometimes used in mathematics to indicate the number of a quantity satisfying some condition, e.g., #{n:n>1}. The symbol is also used to denote a primorial.