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Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

Bertrand's postulate, also called the Bertrand-Chebyshev theorem or Chebyshev's theorem, states that if n>3, there is always at least one prime p between n and 2n-2. ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...

The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1, (1) where ...

The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...