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There exist infinitely many n>0 with p_n^2>p_(n-i)p_(n+i) for all i<n, where p_n is the nth prime. Also, there exist infinitely many n>0 such that 2p_n<p_(n-i)+p_(n+i) for ...

A morphism f:X->Y is said to be separable if K(X) is a separable extension of K(Y).

Let a sequence {a_i}_(i=1)^infty be strictly increasing and composed of nonnegative integers. Call A(x) the number of terms not exceeding x. Then the density is given by ...

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...

An algebraic curve of degree six. Examples include the astroid, atriphtaloid, Cayley's sextic, cornoid, cycloid of Ceva, dumbbell curve, ellipse evolute, epicycloid, Freeth's ...

A transformation in which all points along a given line L remain fixed while other points are shifted parallel to L by a distance proportional to their perpendicular distance ...

A method for constructing magic squares of odd order, also called de la Loubere's method.

Two triangles are similar if their triples of vertex angles are the same.

A system is singular if its condition number is infinite and ill-conditioned if it is too large.

The pedal curve of a sinusoidal spiral r=a[cos(nt)]^(1/n) with pedal point at the center is another sinusoidal spiral with polar equation r=a[cos(nt)]^(1+1/n). A few examples ...