Exercise 1. What is the number of integers between 1 and 10000 that are divisible by 7 and not by 5?
## Solution to Exercise 1

It is the same to look for the number of integers between 1 and 10000 that are divisible by 7 and not by 35.

Among the integers between 1 and 10000, there are 1428 integers divisible by 7 and 285 integers divisible by 35, so the answer is $1428-285=1143$.