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If 1<=b<a and (a,b)=1 (i.e., a and b are relatively prime), then a^n-b^n has at least one primitive prime factor with the following two possible exceptions: 1. 2^6-1^6. 2. ...

Increasing a plane figure's linear dimensions by a scale factor s increases the perimeter p^'->sp and the area A^'->s^2A.

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 ANOVA in which the number of replicates (sets of identical observations) is restricted to be the same for each factor level (treatment group).

A catastrophe which can occur for one control factor and one behavior axis. It is the universal unfolding of the singularity f(x)=x^3 and has the equation F(x,u)=x^3+ux.

A surface harmonic of degree l which is premultiplied by a factor r^l. Confusingly, solid harmonics are also known as "spherical harmonics" (Whittaker and Watson 1990, p. ...

Let X and Y be topological spaces. Then their join is the factor space X*Y=(X×Y×I)/∼, (1) where ∼ is the equivalence relation (x,y,t)∼(x^',y^',t^')<=>{t=t^'=0 and x=x^'; or ; ...

A variant of the Pollard p-1 method which uses Lucas sequences to achieve rapid factorization if some factor p of N has a decomposition of p+1 in small prime factors.

Find two numbers such that x^2=y^2 (mod n). If you know the greatest common divisor of n and x-y, there exists a high probability of determining a prime factor. Taking small ...

A multiple of a number x is any quantity y=nx with n an integer. If x and y are integers, then x is called a factor of y. The smallest positive number m for which there exist ...