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CC
2010
Springer
117views System Software» more  CC 2010»
11 years 2 months ago
Efficiently Certifying Non-Integer Powers
We describe a randomized algorithm that, given an integer a, produces a certificate that the integer is not a pure power of an integer in expected (log a)1+o(1) bit operations unde...
Erich Kaltofen, Mark Lavin
MOC
1998
106views more  MOC 1998»
11 years 5 months ago
Class number bounds and Catalan's equation
We improve a criterion of Inkeri and show that if there is a solution to Catalan’s equation xp − yq = ±1,(1) with p and q prime numbers greater than 3 and both congruent to 3 ...
Ray Steiner
MOC
2002
84views more  MOC 2002»
11 years 5 months ago
On the least prime primitive root modulo a prime
We derive a conditional formula for the natural density E(q) of prime numbers p having its least prime primitive root equal to q, and compare theoretical results with the numerical...
A. Paszkiewicz, Andrzej Schinzel
DM
2008
125views more  DM 2008»
11 years 5 months ago
Difference systems of sets and cyclotomy
Difference Systems of Sets (DSS) are combinatorial configurations that arise in connection with code synchronization. A method for the construction of DSS from partitions of cycli...
Yukiyasu Mutoh, Vladimir D. Tonchev
CSL
2008
Springer
11 years 7 months ago
Proving Infinitude of Prime Numbers Using Binomial Coefficients
We study the problem of proving in weak theories of Bounded Arithmetic the theorem that there are arbitrarily large prime numbers. We show that the theorem can be proved by some &...
Phuong Nguyen
COCO
1999
Springer
101views Algorithms» more  COCO 1999»
11 years 9 months ago
A Lower Bound for Primality
Recent work by Bernasconi, Damm and Shparlinski showed that the set of square-free numbers is not in AC0 , and raised as an open question whether similar (or stronger) lower bound...
Eric Allender, Michael E. Saks, Igor Shparlinski
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