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A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

A test for the primality of Fermat numbers F_n=2^(2^n)+1, with n>=2 and k>=2. Then the two following conditions are equivalent: 1. F_n is prime and (k/F_n)=-1, where (n/k) is ...

A convergence test also called "de Morgan's and Bertrand's test." If the ratio of terms of a series {a_n}_(n=1)^infty can be written in the form ...

A primality test is a test to determine whether or not a given number is prime, as opposed to actually decomposing the number into its constituent prime factors (which is ...

Let sum_(k=1)^(infty)u_k be a series with positive terms, and let rho=lim_(k->infty)u_k^(1/k). 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series ...

If a number fails Miller's primality test for some base a, it is not a prime. If the number passes, it may be a prime. A composite number passing Miller's test is called a ...

Given a series of positive terms u_i and a sequence of positive constants {a_i}, use Kummer's test rho^'=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)) (1) with a_n=n, giving ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...