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In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...

The number of partitions of n in which no parts are multiples of k is sometimes denoted b_k(n) (Gordon and Ono 1997). b_k(n) is also the number of partitions of n into at ...

A d-repdigit is a number composed of repetition of a single digit (in a given base, generally taken as base 10 unless otherwise specified). For example, the beast number 666 ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

A definable set which is the complement of an analytic set.

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

The three diagonal points of a complete quadrilateral are never collinear.

A map x|->x^p where p is a prime.

When all the points P on one line are related by an isometry to all points P^' on another, the midpoints of the segments PP^' are either distinct and collinear or coincident.

Determined the possible values of r and n for which there is an identity of the form (x_1^2+...+x_r^2)(y_1^2+...+y_r^2)=z_1^2+...+z_n^2.