BD TST 2021 NT Exam P1, IMO SL 2021 N1 - Show that $p\mid a_ia_{i+1}a_{i+2}a_{i+3}-i$ for all $i$
Posted: Mon Aug 02, 2021 4:10 pm
Given a positive integer $k$, show that there exists a prime $p$ such that one can choose distinct integers $a_1, a_2, \dots , a_{k+3} \in \{1, 2, \dots, p-1\}$ such that $p$ divides $a_ia_{i+1}a_{i+2}a_{i+3}-i$ for all $i = 1, 2,\dots, k$.