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The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an ...

The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N^2 to 2NlgN, where lg is the ...

A hash function H projects a value from a set with many (or even an infinite number of) members to a value from a set with a fixed number of (fewer) members. Hash functions ...

The Paulus graphs are the 15 strongly regular graphs on 25 nodes with parameters (nu,k,lambda,mu)=(25,12,5,6) and the 10 strongly regular graphs on 26 nodes with parameters ...

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

A (p,q)-torus knot is obtained by looping a string through the hole of a torus p times with q revolutions before joining its ends, where p and q are relatively prime. A ...

The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...