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The modular equation of degree n gives an algebraic connection of the form (K^'(l))/(K(l))=n(K^'(k))/(K(k)) (1) between the transcendental complete elliptic integrals of the ...

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, ...

The Euler-Lagrange differential equation is the fundamental equation of calculus of variations. It states that if J is defined by an integral of the form J=intf(t,y,y^.)dt, ...

A Diophantine problem (i.e., one whose solution must be given in terms of integers) which seeks a solution to the following problem. Given n men and a pile of coconuts, each ...

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

A map projection. The inverse equations for phi are computed by iteration. Let the angle of the projection plane be theta_b. Define a={0 for theta_b=1/2pi; ...

A number which can be represented both in the form x_0^2-Dy_0^2 and in the form Dx_1^2-y_1^2. This is only possible when the Pell equation x^2-Dy^2=-1 (1) is solvable. Then ...

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...

Given the functional (1) find in a class of arcs satisfying p differential and q finite equations phi_alpha(y_1,...,y_n;y_1^',...,y_n^')=0 for alpha=1,...,p ...

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.