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If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, ...

A prime factorization algorithm which uses residues produced in the continued fraction of sqrt(mN) for some suitably chosen m to obtain a square number. The algorithm solves ...

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 ...

In Note M, Burnside (1955) states, "The contrast that these results shew between groups of odd and of even order suggests inevitably that simple groups of odd order do not ...

Mills (1947) proved the existence of a real constant A such that |_A^(3^n)_| (1) is prime for all integers n>=1, where |_x_| is the floor function. Mills (1947) did not, ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

Two angles alpha and beta are said to be complementary if alpha+beta=pi/2. In other words, alpha and beta are complementary angles if they produce a right angle when combined.

Two angles alpha and beta for which alpha+beta=pi are said to be supplementary. In other words, alpha and beta are supplementary angles if they produce a straight angle when ...

The entire function phi(rho,beta;z)=sum_(k=0)^infty(z^k)/(k!Gamma(rhok+beta)), where rho>-1 and beta in C, named after the British mathematician E. M. Wright.

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...