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Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

Form a sequence from an alphabet of letters [1,n] such that there are no consecutive letters and no alternating subsequences of length greater than d. Then the sequence is a ...

Let X be a set of urelements that contains the set N of natural numbers, and let V(X) be a superstructure whose individuals are in X. Let V(^*X) be an enlargement of V(X), ...

An integer whose decimal digits contain no zeros is said to be zerofree. The first few positive zerofree integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I=1) is always in its own class. The ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

The five Mathieu groups M_(11), M_(12), M_(22), M_(23), and M_(24) were the first sporadic groups discovered, having been found in 1861 and 1873 by Mathieu. Frobenius showed ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...