Hard divisibility problem - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-25T10:25:45Z http://mathoverflow.net/feeds/question/95505 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95505/hard-divisibility-problem Hard divisibility problem momo1729 2012-04-29T12:55:47Z 2012-04-29T15:08:58Z <p>The statement of this problem is elementary... How about the proof ? Let $p$ be an odd prime number. For every integer $a$ , define the number </p> <p>$S_{a}=\frac{a}{1}+\frac{a^{2}}{2}+....+\frac{a^{p-1}}{p-1}$.</p> <p>Let $m$ and $n$ be integers such that $S_{3}+S_{4}-3S_{2}=\frac{m}{n}$. Prove that $p$ divides $m$.</p>