Differences

This shows you the differences between two versions of the page.

--- pow:problem4 [2020/03/29 16:27] – created mazur
+++ pow:problem4 [2020/03/30 04:51] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 80% round orange|Problem 4 (due Monday, March 30)>
+Let $p>2$ be an odd prime number. Integers $a_1,a_2,\ldots, a_{p+1}$ in the interval $[0,p]$ have the
+following property: for every permutation $\pi$ of the set $\{1,2,\ldots,p+1\}$ the number
+\[ \sum_{k=1}^{p+1}ka_{\pi(k)}\]
+is not divisible by $p$. Prove that $a_1=a_2=\ldots=a_{p+1}$.
+</box>
+Ashton Keith, a freshman majoring in math, is the only person who solved the problem. His solution is
+based on a different idea than our solution. Both solutions are discussed in the following link {{:pow:2020sproblem4.pdf|Solution}}