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Andrew S. Tanenbaum (OS) Edition 4 Exercise 6 Question 23 (Page No. 467)

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We allocate all process with $m-1$ resources (one less than maximum requirement ).

So if we have $p*(m-1)$ resources we can have deadlock. When we have one more resource its guaranteed to be deadlock free.

So $ r ≥ p(m − 1) + 1$
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