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The recurrence relation (n-1)A_(n+1)=(n^2-1)A_n+(n+1)A_(n-1)+4(-1)^n valid for n=4, 5, ... with A(2)=0 and A(3)=1 and which solves the married couples problem (Dörrie 1965, ...

A coefficient of the Maclaurin series of 1/(ln(1+x))=1/x+1/2-1/(12)x+1/(24)x^2-(19)/(720)x^3+3/(160)x^4+... (OEIS A002206 and A002207), the multiplicative inverse of the ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...

The integral phi(t,u)=int(e^(piitx^2+2piiux))/(e^(2piix)-1)dx which is related to the Jacobi theta functions, mock theta functions, Riemann zeta function, and Siegel theta ...

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

The vector r from the origin to the current position. It is also called the position vector. The derivative of r satisfies ...

A reducible fraction is a fraction p/q such that GCD(p,q)>1, i.e., p/q can be written in reduced form. A fraction that is not reducible is said to be irreducible. For ...

A sorting algorithm which makes n passes over a set of n elements, in each pass selecting the smallest element and deleting it from the set. This algorithm has running time ...

When a prime l divides the elliptic discriminant of a elliptic curve E, two or all three roots of E become congruent (mod l). An elliptic curve is semistable if, for all such ...