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  • 學位論文

多項式時間確定型質數判定演算法的研究

On the AKS Algorithm

指導教授 : 陳其誠
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摘要


本文研究由M. Agrawal, N. Kayal and N. Saxena 提出的第一個多項式時間確定型的質數判定演算法,經過H. Lenstra Jr.等人的建議修改後的版本”PRIMES is in P”(2004),並補充了一些原文裡證明細節。

並列摘要


We take a exposition at the paper “PRIMES is in P” by M. Agrawal, N. Kayal and N. Saxena (2004), in which they used Lenstra's idea and made a revision of their earlier version. We also present some details in the proof.

參考文獻


Granville, A., It Is Easy to Determine Whether a Given Integer Is Prime, Bull. Amer. Math. Soc.42, 3-38, 2005.
M.Nair, On Cheybyshev-type inequalities for primes, Amer. Math. Monthly, 89:126-129, 1982.
E. Fouvry, Theorem de Brun-Titchmarsh; application au theoreme de Fermat, Invent. Math.,79:383-407, 1985.
D. Bernstein, Proving primality in essentially quartic time. http://cr.yp.to/ntheory.html#quartic
DEPARTMENT OF MATHEMATICS, NATIONAL TAIWAN UNIVERSITY, TAIPEI 10764, TAIWAN

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