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## 03. A theorem on sum-free subsets

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!
* To get the current edition of PEN Problems Book, visit here!
* Next week, the solutions will be uploaded here in the pdf file.
* Plus, do not forget to join the group Project PEN in FACEBOOK!