Algorithms aren't new, they can be traced back millennia to Greek mathematicians such as Euclid, the 'father of geometry', who developed an algorithm that became the most efficient method for computing the greatest common divisor
(GCD) of two numbers.
Here we have split each m uniquely into a part that has no common divisor
with n and a part whose prime decomposition uses only the primes of n (note that there is no restriction on the prime powers used; e.g., [m.sub.2] = [n.sup.2] may appear in this decomposition for large enough x).
Chapters discuss the pigeonhole principle, the greatest common divisor
, squares, digital sums, arithmetic and geometric progressions, complementary sequences, quadratic functions and equations, parametric solutions for real equations, the scalar project, equilateral triangles in the complex plane, recurrence relations, sequences given by implicit relations, and matrices associated to second order recurrences.
Smadi  targeted Altera Cyclone IV FPGA family to design an efficient GCD (Greatest Common Divisor
) coprocessor based on Euclid's method with variable datapath sizes.
let, GCD be the greatest common divisor
of screen dimensions SW and SH.
The earliest instances of algorithms include Euclid's function of greatest common divisor
in numerics, Archimedes' approximation of Pi, and Eratosthenes' calculation of prime numbers.
The Euclidean algorithm for finding the greatest common divisor
This type of modular multiplication is closely related to the Euclidean algorithm that determines the greatest common divisor
between two integers by a process of successive division by the remainder from the previous operation.
where [bar.[chi]](a) is a conjugate Dirichlet character modulo q, and (q, a - 1) denotes the greatest common divisor
. Let, as usual, [[gamma].sub.0] denote Euler's constant, and [B.sub.j] stand for the j-th Bernoulli number.
(II) The greatest common divisor
of all cycle lengths is 1.