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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
$${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:{p}\:{is}\:{prime}\:{and}\:{n}\in\mathbb{N},\mathrm{1}<{n}\leqslant{p} \\ $$$${then}\:{pn}−\mathrm{1}\:{is}\:{prime} \\ $$
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.
$${p}=\mathrm{5} \\ $$$${n}=\mathrm{2} \\ $$$${pn}−\mathrm{1}=\mathrm{9} \\ $$$${p}\:\mathrm{is}\:\mathrm{prime}. \\ $$$${pn}−\mathrm{1}=\mathrm{9}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{prime}. \\ $$

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