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?