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A primefree sequence is sequence whose terms are never prime. Graham (1964) proved that there exist relatively prime positive integers a and b such that the recurrence ...

A prolate spheroid is a spheroid that is "pointy" instead of "squashed," i.e., one for which the polar radius c is greater than the equatorial radius a, so c>a (called ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the x-axis, ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

Schur (1916) proved that no matter how the set of positive integers less than or equal to |_n!e_| (where |_x_| is the floor function) is partitioned into n classes, one class ...

Every smooth nonzero vector field on the 3-sphere has at least one closed orbit. The conjecture was proposed in 1950 and proved true for Hopf maps. The conjecture was ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

The trapezo-rhombic dodecahedron, also called the rhombo-trapezoidal dodecahedron, is a general dodecahedron consisting of six identical rhombi and six identical isosceles ...

A fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new ...

A twin prime cluster of order n is a collection of 2n consecutive prime numbers such that consecutive pairs form twin primes. Twin prime clusters were discussed by Mudge ...