\section*{Exercise 2 - 061012}

How many natural numbers \(n<1000\) are there that are neither divisible by 3 nor by 5?
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If \([x]\) denotes the greatest integer not greater than \(x\), then the number of integers less than 1000 that are divisible by 5 is \(\left[\frac{999}{5}\right]=199\).

Similarly, the number of integers divisible by 3 is \(\left[\frac{999}{3}\right]=333\).

However, the numbers that are divisible by both 3 and 5 have been counted twice. Their number is \(\left[\frac{999}{15}\right]=66\).

Thus, out of the 999 numbers, 999 - 333 - \(199+66=533\) numbers are neither divisible by 3 nor by 5.