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Solve the Pell equation x^2-92y^2=1 in integers. The smallest solution is x=1151, y=120.

The mathematical study of the likelihood and probability of events occurring based on known information and inferred by taking a limited number of samples. Statistics plays ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

The circle map is a one-dimensional map which maps a circle onto itself theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n), (1) where theta_(n+1) is computed mod 1 and K is a ...

P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether (Thomson 1869). He categorized knots in ...

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore used in ...

The intersection of two lines L_1 and L_2 in two dimensions with, L_1 containing the points (x_1,y_1) and (x_2,y_2), and L_2 containing the points (x_3,y_3) and (x_4,y_4), is ...

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x)=a_3x^3+a_2x^2+a_1x+a_0. An equation involving a cubic polynomial is called a ...

A quadratic polynomial is a polynomial of degree 2. A univariate quadratic polynomial has the form f(x)=a_2x^2+a_1x+a_0. An equation involving a quadratic polynomial is ...

A mathematical relationship expressing f_n as some combination of f_i with i<n. When formulated as an equation to be solved, recurrence relations are known as recurrence ...