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The Bombieri p-norm of a polynomial Q(x)=sum_(i=0)^na_ix^i (1) is defined by [Q]_p=[sum_(i=0)^n(n; i)^(1-p)|a_i|^p]^(1/p), (2) where (n; i) is a binomial coefficient. The ...

An embedding of a 1-sphere in a 3-manifold which exists continuously over the 2-disk also extends over the disk as an embedding. An alternate phrasing is that if a knot group ...

A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, ...

The central binomial coefficient (2n; n) is never squarefree for n>4. This was proved true for all sufficiently large n by Sárkőzy's theorem. Goetgheluck (1988) proved the ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

A nonnegative measurable function f is called Lebesgue integrable if its Lebesgue integral intfdmu is finite. An arbitrary measurable function is integrable if f^+ and f^- ...

The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the ...

A numeral is a symbol used to represent a number. Arabic numerals (0-9) are the ones most commonly used today. Other types, mainly of historical interest, include Egyptian, ...

The term "porism" is an archaic type of mathematical proposition whose historical purpose is not entirely known. It is used instead of "theorem" by some authors for a small ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...