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The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

Let n be a positive integer and r(n) the number of (not necessarily distinct) prime factors of n (with r(1)=0). Let O(m) be the number of positive integers <=m with an odd ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

A number n is practical if for all k<=n, k is the sum of distinct proper divisors of n. Defined in 1948 by A. K. Srinivasen. All even perfect numbers are practical. The ...

A principal ideal domain is an integral domain in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...

The principal value of an analytic multivalued function is the single value chosen by convention to be returned for a given argument. Complex multivalued functions have ...

Typesetting "errors" in which exponents or multiplication signs are omitted but the resulting expression is equivalent to the original one. Examples include 2^59^2=2592 (1) ...

"Q.E.D." (sometimes written "QED") is an abbreviation for the Latin phrase "quod erat demonstrandum" ("that which was to be demonstrated"), a notation which is often placed ...

"Q.E.F.," sometimes written "QEF," is an abbreviation for the Latin phrase "quod erat faciendum" ("that which was to be done"). It is a translation of the Greek words used by ...

Let ad=bc, then (1) This can also be expressed by defining (2) (3) Then F_(2m)(a,b,c,d)=a^(2m)f_(2m)(x,y), (4) and identity (1) can then be written ...