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If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences x^2=q (mod p) x^2=p (mod q) (1) are both solvable or both unsolvable ...

A problem also known as the points problem or unfinished game. Consider a tournament involving k players playing the same game repetitively. Each game has a single winner, ...

A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...

The tangential mid-arc triangle of a reference triangle DeltaABC is the triangle DeltaA^'B^'C^' whose sides are the tangents to the incircle at the intersections of the ...

A theorem of fundamental importance in spectroscopy and angular momentum theory which provides both (1) an explicit form for the dependence of all matrix elements of ...

An Abelian integral, are also called a hyperelliptic integral, is an integral of the form int_0^x(dt)/(sqrt(R(t))), where R(t) is a polynomial of degree >4.

A property of motion which is conserved to exponential accuracy in the small parameter representing the typical rate of change of the gross properties of the body.

The set A^2 of all ordered pairs of complex numbers.

A nonhomogeneous linear equation or system of nonhomogeneous linear systems of equations is said to be affine.

A knot diagram which has alternating under- and overcrossings as the knot projection is traversed. The first knot which does not have an alternating diagram has 8 crossings.