Teorema_ Lui _ Szemeredi Modificata De Spanu Dumitru Viorel

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Author : Spanu Dumitru Viorel E-mail : [email protected] [email protected] Address :Street Marcu Mihaela Ruxandra no. 5 , 061524 , Bucharest , Romania Phone: +40214131107 0731522216

Author : Spanu Dumitru Viorel

Theorema lui Szemeredi modificata de Spanu Dumitru Viorel . Este evident , conform conjecturilor a 7 –a si The Final Shape of the Sixth Conjecture , ca theorema lui Szemeredi trebuie modificata . Ebosa : Theorema lui Szemeredi modificata de Spanu Dumitru Viorel . Exista multimi cu densitate Banach nula , sau multimi chiar mai putin dense decit multimile cu densitate Banach nula , precum si toate multimile cu upper Banach density pozitiva care contin progresii aritmetice cu k termeni , unde k este un numar natural .

Teorema lui Szemeredi si Teorema Green - Tao sunt incluse in Teorema lui Szemeredi modificata de Spanu Dumitru Viorel . Este evident ca trebuie stabilit un criteriu care sa ne indice care dintre multimile de densitate Banach nula contin progresii aritmetice si care nu contin . Dupa cum am aratat exista multimi chiar mai putin dense decit o multime cu densitate Banach nula si care contine totusi progresii aritmetice arbitrar de lungi (conjectura a 7 – a ) . The largest subset that does not contain a arithmetic progression might be this :

3 term

{1,4,9,16,25,36,49,64,81,100,… ,n2 , … }

.

In fact this subset DOES NOT CONTAIN any arithmetic progression . Author : Spanu Dumitru Viorel It is a proper subset of natural numbers .

Este evident ca nici o multime ale carei elemente ( din care luam doar numerele naturale ) sunt generate de o functie de genul y(x) = ax2 + bx + c

nu contine progresii aritmetice .

Functiile de genul y(n) = an2 + bn + c n€N

,

au o imagine care nu contine progresii aritmetice .

Work in progress .

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