on zero-sum problems
DESCRIPTION
Joseph DiMuro, 12/6/11. On zero-sum problems. An introductory challenge. A zero-sum problem. A zero-sum problem. Outline. Definitions from abstract algebra The zero-sum problem for general groups Variations of the zero-sum problem An application of zero-sum problems. - PowerPoint PPT PresentationTRANSCRIPT
Joseph DiMuro, 12/6/11
An introductory challenge
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A zero-sum problem
A zero-sum problem
Outline
Definitions from abstract algebra The zero-sum problem for general
groups Variations of the zero-sum problem An application of zero-sum problems
Finite abelian groups
Finite abelian groups
Other finite abelian groups
The Davenport constant
Isomorphic abelian groups
Isomorphic abelian groups
Isomorphic abelian groups
Isomorphic abelian groups
Generators:
Isomorphic abelian groups
Isomorphic abelian groups
Isomorphic abelian groups
Isomorphic abelian groups
Finite abelian groups may always be written as direct products of groups of prime power order
Isomorphic abelian groups
The general zero-sum problem
A variation
A variation
A new challenge
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A simple lower bound
Erdös,Ginzburg,Ziv Theorem
Generalizing EGV
Generalizing EGV
Other variations
An application of zero-sum problems Zero-sum problems were used to
show that there are infinitely many Carmichael numbers
Fermat’s “little” theorem
Pseudoprimes
Carmichael numbers
Carmichael numbers
Infinitely many Carmichael numbers
References
Any questions?