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An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

A power series in a variable z is an infinite sum of the form sum_(i=0)^inftya_iz^i, where a_i are integers, real numbers, complex numbers, or any other quantities of a given ...

In 1913, Ramanujan asked if the Diophantine equation of second order 2^n-7=x^2, sometimes called the Ramanujan-Nagell equation, has any solutions other than n=3, 4, 5, 7, and ...

The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...

By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...

The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal epsilon>0, there exists a constant C_epsilon such that for any ...

In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...