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An integer n>1 is said to be highly cototient if the equation x-phi(x)=n has more solutions than the equations x-phi(x)=k for all 1<k<n, where phi is the totient function. ...

A Lehmer number is a number generated by a generalization of a Lucas sequence. Let alpha and beta be complex numbers with alpha+beta = sqrt(R) (1) alphabeta = Q, (2) where Q ...

There are several different definition of link. In knot theory, a link is one or more disjointly embedded circles in three-space. More informally, a link is an assembly of ...

A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively ...

Trigonometric functions of npi/11 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 11 is not a ...

A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

The prime link 05-0201, illustrated above, with braid word sigma_1^2sigma_2^2sigma_1^(-1)sigma_2^(-2) or sigma_1sigma_2^(-1)sigma_1sigma_2^(-2) and Jones polynomial ...

The tribonacci numbers are a generalization of the Fibonacci numbers defined by T_1=1, T_2=1, T_3=2, and the recurrence equation T_n=T_(n-1)+T_(n-2)+T_(n-3) (1) for n>=4 ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...