Question 166
Let $p$ be an odd prime. Does there exist a permutation $a_1, a_2, \dots, a_p$ of $1, 2, \dots, p$ satisfying
$$
(i-j)a_k + (j-k)a_i + (k-i)a_j \neq 0,
$$
for all pairwise distinct $i, j, k$?
$$
(i-j)a_k + (j-k)a_i + (k-i)a_j \neq 0,
$$
for all pairwise distinct $i, j, k$?