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A method for verifying the correctness of an arithmetical operation on natural numbers, based on the same principle as casting out nines. The methods of sevens takes ...

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

Catalan (1876, 1891) noted that the sequence of Mersenne numbers 2^2-1=3, 2^3-1=7, and 2^7-1=127, and (OEIS A007013) were all prime (Dickson 2005, p. 22). Therefore, the ...

Special cases of general formulas due to Bessel. J_0(sqrt(z^2-y^2))=1/piint_0^pie^(ycostheta)cos(zsintheta)dtheta, where J_0(z) is a Bessel function of the first kind. Now, ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

The dual polyhedra of the Archimedean solids, given in the following table. They are known as Catalan solids in honor of the Belgian mathematician who first published them in ...

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted K ...