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For an integer n>=2, let lpf(n) denote the least prime factor of n. A pair of integers (x,y) is called a twin peak if 1. x<y, 2. lpf(x)=lpf(y), 3. For all z, x<z<y implies ...

The dihedral group D_4 is one of the two non-Abelian groups of the five groups total of group order 8. It is sometimes called the octic group. An example of D_4 is the ...

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

A group action G×Omega->Omega might preserve a special kind of partition of Omega called a system of blocks. A block is a subset Delta of Omega such that for any group ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...

A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...