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A friend of a number n is another number m such that (m,n) is a friendly pair.

Almost all natural numbers are very, very, very large (Steinbach 1990, p. 111).

Let F be a field of field characteristic p. Then the Frobenius automorphism on F is the map phi:F->F which maps alpha to alpha^p for each element alpha of F.

If f^'(x) is continuous and the integral converges, int_0^infty(f(ax)-f(bx))/xdx=[f(0)-f(infty)]ln(b/a).

A finite extension K=Q(z)(w) of the field Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0+a_1alpha+a_2alpha^2+...+a_nalpha^n, where ...

A function between categories which maps objects to objects and morphisms to morphisms. Functors exist in both covariant and contravariant types.

A game which permits a draw ("tie") when played properly by both players. Tic-tac-toe, for example, is a futile game.

Let G be a group and S be a set. Then S is called a left G-set if there exists a map phi:G×S->S such that phi(g_1,phi(g_2,s))=phi(g_1g_2,s) for all s in S and all g_1,g_2 in ...

A set S is said to be GCD-closed if GCD(x_i,x_j) in S for 1<=i,j<=n.

A separable algebraic extension E of F for which every irreducible polynomial in F which has a single root in E has all its roots in E is said to be Galoisian. Galoisian ...