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A generalization of Fermat's little theorem. Euler published a proof of the following more general theorem in 1736. Let phi(n) denote the totient function. Then a^(phi(n))=1 ...

A root-finding algorithm also known as the tangent hyperbolas method or Halley's rational formula. As in Halley's irrational formula, take the second-order Taylor series ...

A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...

Let U(P,Q) and V(P,Q) be Lucas sequences generated by P and Q, and define D=P^2-4Q. (1) Then {U_((n-(D/n))/2)=0 (mod n) when (Q/n)=1; V_((n-(D/n))/2)=D (mod n) when (Q/n)=-1, ...

An interior point method is a linear or nonlinear programming method (Forsgren et al. 2002) that achieves optimization by going through the middle of the solid defined by the ...

A lucky number of Euler is a number p such that the prime-generating polynomial n^2-n+p is prime for n=1, 2, ..., p-1. Such numbers are related to the imaginary quadratic ...

The second part of Pollard rho factorization method concerns detection of the fact that a sequence has become periodic. Pollard's original suggestion was to use the idea ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

Caesar's method is an encryption scheme involving shifting an alphabet (so a->c, b->d, c->e, d->f, etc., x->z,y->a,z->b). It is one of the most basic encryption methods, and ...

A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...