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        riddles >> easy >> Prime Works
        
(Message started by: The_Fool on Mar 8^th, 2004, 10:06am)

Title: Prime Works
Post by The_Fool on Mar 8^th, 2004, 10:06am

is it possible for (p^2+q^2)/(pq) to be an integer when p does not equal q? When p=q, it's 2. What about when their not?

Title: Re: Prime Works
Post by Sir Col on Mar 8^th, 2004, 10:19am

Assuming you meant p,q are prime...

::[hide]
If (p²+q²)/(pq)=r, where r is integer, we get p²+q²=pqr.

As p divides RHS, p must divide LHS. However, q and p are different, so p cannot divide q. Hence there is no solution.
[/hide]::

[e] I thought this was familiar and did a quick search. It seems that I started a thread, asking the more general question about the case where p and q are not necessarily prime...
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1073053801 [/e]