Primality Testing Using Complex Integers and Pythagorean Triplets

Some Results concerning Pythagorean Triplets

By using a computer program devised by M. Creutz, we were able to determine all Pythagoeran triplets for which z ^ 300. At this point, a distinction must must be made between P-triplets for which x9 y9 and z have no common divisor [the so-called "primitive solutions" of (1)] and P-triplets which are related to the primitive solutions by multiplication by a common integer factor k. So, if Xi9y^9...

Trisection, Pythagorean Angles, and Gaussian Integers

Pythagorean angles, that is angles with rational sines and cosines, provide an interesting environment for studying the question of characterizing trisectable angles. The main result of this paper shows that a Pythagorean angle is trisectable if and only if it is three times some other Pythagorean angle. Using the Euclidean parametrization of Pythagorean angles, this result allows an effective ...

Primality testing

Primality Testing

Prime numbers are extremely useful, and are an essential input to many algorithms in large part due to the algebraic structure of arithmetic modulo a prime. In everyday life, perhaps the most frequent use for prime numbers is in RSA encryption, which requires quite large primes (typically≥ 128-bits long). Fortunately, there are lots of primes—for large n, the probability that a random integer l...

Algorithmic Primality Testing

This project consists of the implementation and analysis of a number of primality testing algorithms from Chapter 9 of 3]. The rst algorithm is added to provide a point of comparison and the section on Lucas-Lehmer testing was derived mainly from material found in 4]. Aside from simply implementing these tests in Maple and C, the goal of this paper is to provide a somewhat simpliied and more ge...