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In the American system, 10^(51).

In the American system, 10^(21).

An algorithm which finds the least nonnegative value of sqrt(a (mod p)) for given a and prime p.

A translation without rotation or distortion.

The edge of a polygon or face of a polyhedron are sometimes called sides.

Theta(G;A)=<theta(a):a in A-1> is an A-invariant solvable p^'-subgroup of G.

To multiply the size of a d-D object by a factor a, c=a^d copies are required, and the quantity d=(lnc)/(lna) is called the similarity dimension.

An algebra with no nontrivial ideals.

If (sinalpha)/(sinbeta)=m/n, then (tan[1/2(alpha-beta)])/(tan[1/2(alpha+beta)])=(m-n)/(m+n).

rho_(2s)(n)=(pi^s)/(Gamma(s))n^(s-1)sum_(p,q)((S_(p,q))/q)^(2s)e^(2nppii/q), where S_(p,q) is a Gaussian sum, and Gamma(s) is the gamma function.