Question Number 475 by 123456 last updated on 25/Jan/15
![proof or given a counter example: if p is prime and n∈N,1<n≤p then pn−1 is prime](https://www.tinkutara.com/question/Q475.png)
$${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:{p}\:{is}\:{prime}\:{and}\:{n}\in\mathbb{N},\mathrm{1}<{n}\leqslant{p} \\ $$$${then}\:{pn}−\mathrm{1}\:{is}\:{prime} \\ $$
Answered by prakash jain last updated on 11/Jan/15
![p=5 n=2 pn−1=9 p is prime. pn−1=9 is not a prime.](https://www.tinkutara.com/question/Q477.png)
$${p}=\mathrm{5} \\ $$$${n}=\mathrm{2} \\ $$$${pn}−\mathrm{1}=\mathrm{9} \\ $$$${p}\:\mathrm{is}\:\mathrm{prime}. \\ $$$${pn}−\mathrm{1}=\mathrm{9}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{prime}. \\ $$