Latios Posted January 8, 2005 Share Posted January 8, 2005 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. Link to comment Share on other sites More sharing options...
matt grime Posted January 8, 2005 Share Posted January 8, 2005 no, there are no solutions, in fact N can be any non-perfect square and there are no solutions. Link to comment Share on other sites More sharing options...
Latios Posted January 8, 2005 Author Share Posted January 8, 2005 So would that in turn indicate that all prime numbers have irrational roots? And what's the reason that equation has no solution? Link to comment Share on other sites More sharing options...
matt grime Posted January 9, 2005 Share Posted January 9, 2005 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. Link to comment Share on other sites More sharing options...
Latios Posted January 10, 2005 Author Share Posted January 10, 2005 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? Link to comment Share on other sites More sharing options...
matt grime Posted January 10, 2005 Share Posted January 10, 2005 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. Link to comment Share on other sites More sharing options...
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