Let \(a\), \(b\) be distinct positive integers. Prove that there exists a prime \(p\) such that when dividing both \(a\) and \(b\) by \(p\), the remainder of \(a\) is less than the remainder of \(b\).

The best solution was submitted by 이종원 (2014학번). Congratulations!

Alternative solutions were submitted by 황성호 (+3), 정성진(+2), 박훈민 (+2). There were a few incorrect submissions (KSJ, JKJ, KDS, AHS, KKS, PKH).