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The Banach density of a set A of integers is defined as lim_(d->infty)max_(n)(|{A intersection [n+1,...,n+d]}|)/d, if the limit exists. If the lim is replaced with lim sup or ...

If a and b are integers not both equal to 0, then there exist integers u and v such that GCD(a,b)=au+bv, where GCD(a,b) is the greatest common divisor of a and b.

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).

There exists a total computable predicate P such that for any algorithm computing P(x) with running time T(x), there exists another algorithm computing P(x) with computation ...

Define E(x;q,a)=psi(x;q,a)-x/(phi(q)), (1) where psi(x;q,a)=sum_(n<=x; n=a (mod q))Lambda(n) (2) (Davenport 1980, p. 121), Lambda(n) is the Mangoldt function, and phi(q) is ...

A Brauer chain is an addition chain in which each member uses the previous member as an addend. A number n for which a shortest chain exists which is a Brauer chain is called ...

A number n for which a shortest chain exists which is a Brauer chain is called a Brauer number. There are infinitely many non-Brauer numbers.

A Brunnian link is a set of n linked loops such that each proper sublink is trivial, so that the removal of any component leaves a set of trivial unlinked unknots. The ...

Let K_1 be a torus knot. Then the satellite knot with companion knot K_2 is a cable knot on K_2.

If bc=bd (mod a) and (b,a)=1 (i.e., a and b are relatively prime), then c=d (mod a).