Comments on Search Procedures for Primitive Roots 1721
نویسنده
چکیده
Let p be an odd prime. Assuming the Extended Riemann Hypothesis , we show how to construct O((log p) 4 (loglogp) ?3) residues modulo p, one of which must be a primitive root, in deterministic polynomial time. Granting some well-known character sum bounds, the proof is elementary, leading to an explicit algorithm.
منابع مشابه
Comments on search procedures for primitive roots
Let p be an odd prime. Assuming the Extended Riemann Hypothesis, we show how to construct O((log p)4(log log p)−3) residues modulo p, one of which must be a primitive root, in deterministic polynomial time. Granting some well-known character sum bounds, the proof is elementary, leading to an explicit algorithm.
متن کاملA generalized Mobius transform, arithmetic Fourier transforms, and primitive roots
A general approach to arithmetic Fourier transforms is developed. The implementation is based on sine and cosine killer procedures pertaining to a generalized Möbius transform involving reduced periodic multiplicative arithmetical functions. It is shown that cosine killer procedures exist whenever one half of Euler’s totient function of the order of the transform is odd. Primitive roots and ind...
متن کاملFinding Primitive Roots Pseudo-Deterministically
Pseudo-deterministic algorithms are randomized search algorithms which output unique solutions (i.e., with high probability they output the same solution on each execution). We present a pseudo-deterministic algorithm that, given a prime p, finds a primitive root modulo p in time exp(O( p log p log log p)). This improves upon the previous best known provable deterministic (and pseudo-determinis...
متن کاملA Typology of Supervisor Written Feedback on L2 Students’ Theses/Dissertations
The present study aimed at providing a typology of Iranian supervisors’ written feedback on L2 graduate students’ theses/dissertations and examining the way different speech functions are employed to put the supervisors’ thoughts and feelings into words. In so doing, a corpus of comments, including 15,198 comments provided on 87 TEFL theses and dissertations by 30 supervisors were analyzed. We ...
متن کاملUsing Greedy Randomize Adaptive Search Procedure for solve the Quadratic Assignment Problem
Greedy randomize adaptive search procedure is one of the repetitive meta-heuristic to solve combinatorial problem. In this procedure, each repetition includes two, construction and local search phase. A high quality feasible primitive answer is made in construction phase and is improved in the second phase with local search. The best answer result of iterations, declare as output. In this stu...
متن کامل