A powerful algorithm named for one of these objects has an asymptotic runtime of the form "exponential of cuberoot log n times two-thirds power of log log n", with a constant factor equal to "the cube root of sixty-four ninths".
One technique named for one of these objects begins by identifying some number of numbers such that their squares modn are smooth with respect to the factor base, where n is the input to the technique. That technique, developed by Pomerance,proceeds by fiÂnding the modular roots of the quadratic polynomial "x squared minus n", often using the Tonelli-Shanksmethod. A powerful algorithm named for one of these objects has an asymptotic runtime of the form "exponential of cuberoot log n times two-thirds power of log log n", with a constant factor equal to "the cube root of sixty-four ninths". Thatalgorithm is the best known classical factoring algorithm for arbitrary numbers besides prime powers, and is known as the"quadratic" variant of this object. The prototypical object of this name, a variant of which was developed by Atkin, is constructedby iteratively marking o multiples of prime numbers. For 10 points, give this term that describes an invention ofEratosthenes.
One technique named for one of these objects begins by identifying some number of numbers such that their squares modn are smooth with respect to the factor base, where n is the input to the technique.
sieve