Question 42
Prove that there exists a sequence of positive integers $x_1, x_2, \dots, x_n, \dots$ that satisfies the following two conditions:
(i) contains each of the positive integers exactly once,
(ii) for each $n=1,2,\dots$ the partial sum $x_1 + x_2 + \dots + x_n$ is divisible by $n!$.
(i) contains each of the positive integers exactly once,
(ii) for each $n=1,2,\dots$ the partial sum $x_1 + x_2 + \dots + x_n$ is divisible by $n!$.