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Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

The rhombic triacontahedron is a zonohedron which is the dual polyhedron of the icosidodecahedron A_4 (Holden 1971, p. 55). It is Wenninger dual W_(12). It is composed of 30 ...

Five or six Wolf prizes are awarded yearly to outstanding living scientists and artists for achievements in the interest of mankind and friendly relations among peoples. In ...

There exists an integer N such that every string in the look and say sequence "decays" in at most N days to a compound of "common" and "transuranic elements." The table below ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. ...

A plane figure or solid compound consisting of multiple connected copies of a given base shape. For example, affixing n equal squares gives an n-polyomino, while affixing n ...

The chord through a focus parallel to the conic section directrix of a conic section is called the latus rectum, and half this length is called the semilatus rectum (Coxeter ...

Eternity is a puzzle devised by Christopher Monckton and consisting of 209 pieces, each of which is a 12-polydrafter (i.e., a compound of 30-60-90 triangles). The puzzle was ...