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The least number of unknotted arcs lying above the plane in any projection. The knot 05-002 has bridge number 2. Such knots are called 2-bridge knots. There is a one-to-one ...

The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

A congruent number can be defined as an integer that is equal to the area of a rational right triangle (Koblitz 1993). Numbers (a,x,y,z,t) such that {x^2+ay^2=z^2; ...

An L-algebraic number is a number theta in (0,1) which satisfies sum_(k=0)^nc_kL(theta^k)=0, (1) where L(x) is the Rogers L-function and c_k are integers not all equal to 0 ...

If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed ...

A Stoneham number is a number alpha_(b,c) of the form alpha_(b,c)=sum_(k=1)^infty1/(b^(c^k)c^k), where b,c>1 are relatively prime positive integers. Stoneham (1973) proved ...

A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

An odd alternating permutation number, more commonly called an Euler number or secant number.

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...