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