January | 2008 | Project PEN

Archive for January, 2008

03. A theorem on sum-free subsets

Posted in Problem of the Bi-Week on January 30, 2008| Leave a Comment »

Here goes the problem:

03. PEN O53 (Schur Theorem) Suppose the set $M=\{1,2,\ldots,n\}$ is partitioned into $t$ disjoint subsets $M_1,\ldots,M_t$ . Show that if $n\ge\lfloor t!\cdot e\rfloor$ then at least one class $M_z$ contains three elements $a,b,c$ with the property that $a+b=c$ .

Next week, you will be presented two different solutions and several related results.

* Any comments are welcome! You can also disscuss the problem here!
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* Next week, the solutions will be uploaded here in the pdf file.
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