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The determinant of a binary quadratic form Au^2+2Buv+Cv^2 is defined as D=AC-B^2. It is equal to 1/4 of the corresponding binary quadratic form discriminant. Unfortunately, ...

The discriminant of a binary quadratic form au^2+buv+cv^2 is defined by d=4ac-b^2. It is equal to four times the corresponding binary quadratic form determinant. ...

An algorithm for computing an Egyptian fraction (Stewart 1992).

The two recursive sequences U_n = mU_(n-1)+U_(n-2) (1) V_n = mV_(n-1)+V_(n-2) (2) with U_0=0, U_1=1 and V_0=2, V_1=m, can be solved for the individual U_n and V_n. They are ...

If M^3 is a closed oriented connected 3-manifold such that every simple closed curve in M lies interior to a ball in M, then M is homeomorphic with the hypersphere, S^3.

The ordinary differential equation (y^')^m=f(x,y) (Hille 1969, p. 675; Zwillinger 1997, p. 120).

A ruled surface M is said to be a binormal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vB^^(u), where B is the binormal vector.

If two complementary Plücker characteristics are equal, then each characteristic is equal to its complement except in four cases where the sum of order and class is 9.

The image of A_5×A_5 in the special orthogonal group SO(4), where A_5 is the icosahedral group.

If there is an integer x such that x^4=q (mod p), then q is said to be a biquadratic residue (mod p). If not, q is said to be a biquadratic nonresidue (mod p).