A number theory problem by Akshat Sharda

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

Find the number of positive integers \(≤10000\) which are simultaneously \(7-\text{safe}, 11-\text{safe}\) and \(13-\text{safe}\).

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