Prime numbers roots
 
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[Solved] Prime numbers roots

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If p, q are prime numbers and satisfy  5p+3q=19. 

Compute the value of \frac{1}{\sqrt{q}-\sqrt{p}}.

 

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The equation  \large 5p+3q=19    implies that one of p, q is even. Since p, q are prime numbers and the only even prime number is 2, we have two possibilities: If q = 2, then p=13/5, not a prime number, so this case is impossible; if p=2, then q=3, thus \large \frac{1}{\sqrt{q}-\sqrt{p}}=\frac{1}{\sqrt{3}-\sqrt{2}}=\sqrt{3}+\sqrt{2} 

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