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Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A prime link is a link that cannot be represented as a knot sum of other links. Doll and Hoste (1991) list polynomials for oriented links of nine or fewer crossings, and ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors (excluding 1). (The primes are excluded since they trivially ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

The Doyle graph, sometimes also known as the Holt graph (Marušič et al. 2005), is the quartic symmetric graph on 27 nodes illustrated above in several embeddings. It is ...

A Latin square is said to be odd if it contains an odd number of rows and columns that are odd permutations. Otherwise, it is said to be even. Let the number of even Latin ...

In general, an icosidodecahedron is a 32-faced polyhedron. A number of such solids are illustrated above. "The" (quasiregular) icosidodecahedron is the 32-faced Archimedean ...