## 08S An arithmetic partition

April 17, 2008 by compactorange

08. PEN O 35 ( Romania TST 1998 )

Let be a prime number and be integers.

Prove that is an arithmetic progression if and only if there exists a partition of into sets such that

where denotes the set .

Here is the official solution file: PEN08S

You can also disscuss the problems here!

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