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An integer sequence given by the recurrence relation a(n)=a(a(n-2))+a(n-a(n-2)) with a(1)=a(2)=1. The first few values are 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

The quartic formula is a name sometimes given to one of the related explicit formulas for the four roots z_1, ..., z_4 of an arbitrary quartic equation with real coefficients ...

A set of m distinct positive integers S={a_1,...,a_m} satisfies the Diophantus property D(n) of order n (a positive integer) if, for all i,j=1, ..., m with i!=j, ...

An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

Pre-Calculus

Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

A generalization of the equation whose solution is desired in Fermat's last theorem x^n+y^n=z^n to x^n+y^n=cz^n for x, y, z, and c positive constants, with trivial solutions ...