MathDB

Suppose that the set

M=\{1,2,\cdots,n\}

is split into

t

disjoint subsets

M_{1}

\cdots

M_{t}

where the cardinality of

M_i

m_{i}

, and

m_{i} \ge m_{i+1}

, for

i=1,\cdots,t-1

. Show that if

n>t!\cdot e

then at least one class

M_z

contains three elements

x_{i}

x_{j}

x_{k}

with the property that

x_{i}-x_{j}=x_{k}

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