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Prime Problem

Latios
in Mathematics

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Is there a particular solution to this equation:

 

N=p^2/q^2, where N is any prime number and p and q are two intergers.

no, there are no solutions, in fact N can be any non-perfect square and there are no solutions.

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So would that in turn indicate that all prime numbers have irrational roots? And what's the reason that equation has no solution?

the reasons there are no solutions are quite trivial, and i suggest you try and figure them out yourself: rearrajngee and think about prime decomposition.

  • Author

I am not too good with prime number theorems, so I have no idea how to find a proof for this equation. Can you point me to a ceratin direction or give me a web site on the topic please?

Did you rearrange the equation and think about how many prime factors are on each side if N is not a perfect square? On one side it's an even number, and on the other it's odd.

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