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comment Dubiety About An Inequality Proof
Whoops, he specifies that $xy > 0$ if $x \in F$, $y \in F$, where $F$ is an ordered field, and $x >0$ and $y > 0$...I reckon more careful reading elucidates all answers...
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comment Four Isosceles Trapezoids
Oh, wait! When I wrote the problem statement, I forgot to write that $x$ and $y$ are assumed to be positive integers. How does that change things? Could I immediately infer that $\displaystyle A = \frac{y+x}{2} \cdot \frac{y-x}{2}$ means that $A$ has to be factored into two positive integers?
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comment Four Isosceles Trapezoids
I do not understand why I have to argue that $\frac{y+x}{x}$ and $\frac{y-x}{2}$ must be integers. I want them to be integers, so I compel them to be integers; and for each fraction to evaluate to an integer, the numerator must be some multiple of $2$. Is this the sort of proof you had in mind? If not, I do not see how it is possible to prove that they must be integers.
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