Originally Posted by Jameson
Open parantheses,
=
Thus, we have,
(1)
(2)
(3)
(4)
Now multiply (2)(3)(4) to get,
Thus,
The reason being that,
and all thus, they are not squares. Then, .
Here is an outline of the proof, to keep thing simple let us do it with only two terms,
and are positive integers with a non-square.
Now if then,
Thus,
Impossible because LHS is irrational.
If you have, you get the same thing.
Thus, which implies that
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