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--- pow:problem7s25 [2025/05/11 00:53] – created mazur
+++ pow:problem7s25 [2025/05/13 14:54] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange| Problem 7 (due Monday, May 12 )>
+Let $p$ be a prime number and $k<p$ a positive integer. Let $m=\left\lceil \frac{p}{k+1}\right\rceil$.
+Show that there is a set $A\subseteq\{1,2,\ldots, p-1\}$ with at most 2m elements such that
+for every $a\in\{1,2,\ldots,p-1\}$ there are $b\in A$ and $c\in\{1,2,\ldots,k\}$ such that
+$p$ divides $a-bc$.
+</box>
+No solutions were submitted. For a detailed
+solution see the following link {{:pow:2025sproblem7.pdf|Solution}}.