Safety first

For a positive integer \(p\), define the positive integer \(n\) to be \(p\)-safe if \(n\) differs in absolute value by more than 2 from all multiples of \(p\). For example, the set of 10-safe numbers includes \(\{3, 4, 5, 6, 7, 13, 14, 15, 16, 17\}\).

Find the number of positive integers less than or equal to 10 000 which are simultaneously 7-safe, 11-safe, and 13-safe.

×

Problem Loading...

Note Loading...

Set Loading...