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 .
The problem is from Romanian TST 1998 and was proposed by Vasile Pop.
You can find it here. I remember I spend so much time solving and writing the second solution in the pdf. Good old days when I had time to write for PEN . Actually, not even now am I sure if that solution is fully corect. I really wonder if anyone has solved it during the TST. Valentin, any information?
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. Actually, not even now am I sure if that solution is fully corect. I really wonder if anyone has solved it during the TST. Valentin, any information? 
