I dont understand how to this problem Please show me and inc

I dont understand how to this problem.. Please show me and include your answer. Thank you!

Exercise 2.14 iven any integer n 1, show that there exists an integer, whose digits are all either 0 or 1, that is divisible by n. (Hint: you know that if you take any set of n 1 integers, the difference of some two of them must be divisible by n. Now t to choose your set of n 1 integers carefully!

Solution

Let the (n+1) integers be 1,11,111,1111.....11111(n+1)s

When divided by n they leave n+1 remainders and by the4 pigeon hole principle two of these remainders were equal.

So, the difference of these integers gives the integers of the form 1111......000000

Hence divisible by n