# Thread: A much needed proof

1. ## A 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)

2. Originally Posted by gentsl
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)

No it means that if you set $a_1=a_2= .. =a_k=\sqrt{n}$ then the left hand side equals $k\sqrt{n}$ and the right hand side is equal to $n \left(\frac{k}{\sqrt{n}}\right)=k\sqrt{n}$, so the condition of the problem is satisfied by these values (at least it is when $n$ is a perfect square, otherwise the $a$'s are not integers and we still need a solution).