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NP and Mathematics  a computational complexity perspective
 Proc. of the ICM 06
"... “P versus N P – a gift to mathematics from Computer Science” ..."
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“P versus N P – a gift to mathematics from Computer Science”
A GENERALIZATION OF MILLER’S PRIMALITY THEOREM PEDRO BERRIZBEITIA AND AURORA OLIVIERI
"... Abstract. For any integer r we show that the notion of ωprime to base a introduced by Berrizbeitia and Berry, 2000, leads to a primality test for numbers n congruent to 1 modulo r, which runs in polynomial time assuming the Extended Riemann Hypothesis (ERH). For r = 2 we obtain Miller’s classical r ..."
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Abstract. For any integer r we show that the notion of ωprime to base a introduced by Berrizbeitia and Berry, 2000, leads to a primality test for numbers n congruent to 1 modulo r, which runs in polynomial time assuming the Extended Riemann Hypothesis (ERH). For r = 2 we obtain Miller’s classical result. 1.
A note on Agrawal conjecture
"... Abstract. We prove that Lenstra proposition suggesting existence of many counterexamples to Agrawal conjecture is true in a more general case. At the same time we obtain a strictly ascending chain of subgroups of the group (Zp[X]/(Cr(X))) * and state the modified conjecture that the set {X1, X+2} ..."
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Abstract. We prove that Lenstra proposition suggesting existence of many counterexamples to Agrawal conjecture is true in a more general case. At the same time we obtain a strictly ascending chain of subgroups of the group (Zp[X]/(Cr(X))) * and state the modified conjecture that the set {X1, X+2} generate big enough subgroup of this group. 1
TEST DE PRIMALITÉ AKS ET APPLICATIONS
"... Abstract. Les mathématiques ont tenté jusqu’à ce jour de découvrir une régularité dans la suite des nombres premiers, et nous avons de bonnes raisons de croire qu’il y a là un mystère que l’esprit humain ne pénétrera jamais. Il suffit d’ailleurs, pour s’en convaincre, de jeter un regard sur une tabl ..."
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Abstract. Les mathématiques ont tenté jusqu’à ce jour de découvrir une régularité dans la suite des nombres premiers, et nous avons de bonnes raisons de croire qu’il y a là un mystère que l’esprit humain ne pénétrera jamais. Il suffit d’ailleurs, pour s’en convaincre, de jeter un regard sur une table de nombres premiers (que certains ont pris la peine de calculer jusqu’à plusieurs centaines de milliers); on est alors instantanément convaincu qu’il n’y règne ni loi, ni ordre, ni règle. Leonhard Euler (17071783) 1.
MATHEMATICAL ENGINEERING TECHNICAL REPORTS
, 2007
"... Generalized zigzag products of regular digraphs and bounds on their spectral expansions ..."
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Generalized zigzag products of regular digraphs and bounds on their spectral expansions
RP3
"... Abstract — We implement the AgrawalKayalSaxena primality testing algorithm. We discuss optimizations to the implementation that resulted in improved performance over the initial implementation. We further discuss methods of obtaining faster runtimes for candidate primes of increasing size. ..."
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Abstract — We implement the AgrawalKayalSaxena primality testing algorithm. We discuss optimizations to the implementation that resulted in improved performance over the initial implementation. We further discuss methods of obtaining faster runtimes for candidate primes of increasing size.