Archive for February 7th, 2008

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.

Here is the official solution file: PEN03S
You can also disscuss the problems here!

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