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The Frobenius number is the largest value b for which the Frobenius equation a_1x_1+a_2x_2+...+a_nx_n=b, (1) has no solution, where the a_i are positive integers, b is an ...

Let p>3 be a prime number, then 4(x^p-y^p)/(x-y)=R^2(x,y)-(-1)^((p-1)/2)pS^2(x,y), where R(x,y) and S(x,y) are homogeneous polynomials in x and y with integer coefficients. ...

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 ...

The inhomogeneous Helmholtz differential equation is del ^2psi(r)+k^2psi(r)=rho(r), (1) where the Helmholtz operator is defined as L^~=del ^2+k^2. The Green's function is ...

The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

The sequence defined by G(0)=0 and G(n)=n-G(G(n-1)). (1) The first few terms for n=1, 2, ... are 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, ... (OEIS A005206). This can be ...

The pair of sequences defined by F(0)=1, M(0)=0, and F(n) = n-M(F(n-1)) (1) M(n) = n-F(M(n-1)). (2) The first few terms of the "male" sequence M(n) for n=0, 1, ... are 0, 0, ...

A generalization of the Fibonacci numbers defined by the four constants (p,q,r,s) and the definitions H_0=p and H_1=q together with the linear recurrence equation ...

A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...

A system of coordinates obtained by inversion of the prolate spheroids and two-sheeted hyperboloids in prolate spheroidal coordinates. The inverse prolate spheroidal ...