- #1
Echo8
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Homework Statement
Find all positive integers n such that both n + 2008 divides n^2 + 2008 and n + 2009 divides n^2 + 2009
Homework Equations
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The Attempt at a Solution
I have no idea where to start... I'm not even sure it's a sequence and series question. If it is then I have no idea what to do.
I've played around with it by saying (n^2+2008)/(n+2008)=a and (n^2+2009)/(n+2009)=b, rearranging them into quadratics and equating them, then rearranging again in terms of n. Doing this I got n=(-2008a+2009b-1)/(a-b) and couldn't see anything to do from this. I did a similar thing using partial fractions but ended up with pretty much the same equation (though not exactly the same so I could well have done something wrong but I don't think that was the right way to go about it anyway).
Any light that anyone can shed on this would be much appreciated :)