Solve the equation [tex]np_n+(n+1)p_{n+1}+(n+2)p_{n+2}=p^2_{n+2}[/tex] where [tex]n\in \mathbb N^*[/tex] and [tex]p_n , p_{n+1} , p_{n+2}[/tex] are three consecutive prime numbers.
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A solution is [tex]n=2,p_2=3,p_3=5,p_4=7.[/tex]
May be other solutions?
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A solution is [tex]n=2,p_2=3,p_3=5,p_4=7.[/tex]
May be other solutions?