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A representation phi of a group G is faithful if it is one-to-one, i.e., if phi(g)=phi(h) implies g=h for g,h in G. Equivalently, phi is faithful if phi(g)=I_n implies g=e, ...

The Diophantine equation x^n+y^n=z^n. The assertion that this equation has no nontrivial solutions for n>2 has a long and fascinating history and is known as Fermat's last ...

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...

The field of rationals is the set of rational numbers, which form a field. This field is commonly denoted Q (doublestruck Q).

A ring equipped with a filtration.

A set which contains a nonnegative integral number of elements is said to be finite. A set which is not finite is said to be infinite. A finite or countably infinite set is ...

An entire function f is said to be of finite order if there exist numbers a,r>0 such that |f(z)|<=exp(|z|^a) for all |z|>r. The infimum of all numbers a for which this ...

Let D be a planar Abelian difference set and t be any divisor of n. Then t is a numerical multiplier of D, where a multiplier is defined as an automorphism alpha of a group G ...

The statistical index P_B=sqrt(P_LP_P), where P_L is Laspeyres' index and P_P is Paasche's index.

A balanced incomplete block design (v, k, lambda, r, b) exists only for b>=v (or, equivalently, r>=k).