Given integer n>1, prove that we can find integer k>1 and a1, a2, ......ak >1 such that

a1 + a2 +........ak = n(1/a1 + 1/a2 +....1/ak)

Does this need some complex theorem to start with? Much thanks!

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- Nov 6th 2007, 11:56 PMgentslA much needed proof
Given integer n>1, prove that we can find integer k>1 and a1, a2, ......ak >1 such that

a1 + a2 +........ak = n(1/a1 + 1/a2 +....1/ak)

Does this need some complex theorem to start with? Much thanks! - Nov 7th 2007, 09:52 AMThePerfectHacker
- Nov 8th 2007, 01:39 PMgentsl
This means n = +/- sqrt a_k therefore k >1 must apply ? smilarly for a1 + a2 +........ak = n(1/a1 + 1/a2 +....1/ak)?

- Nov 10th 2007, 10:05 AMCaptainBlack
No it means that if you set then the left hand side equals and the right hand side is equal to , so the condition of the problem is satisfied by these values (at least it is when is a perfect square, otherwise the 's are not integers and we still need a solution).

RonL