Indicate a six-digit number $N$, consisting of different digits, such that the numbers $2 N, 3 N, 4 N, 5 N, 6 N$ differ from it by a permutation of digits.
Consider the period of the fraction $1 / 7$.

## Solution

Let's take $N=142857$. A direct check shows that $2N=285714, 3N=428571, 4N=571428, 5N$ $=714285, 6N=857142$.

## Answer

$N=142857$.