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 Dec 22 asked Dubiety About An Inequality Proof Dec 19 awarded Constituent Dec 15 awarded Famous Question Dec 9 awarded Caucus Dec 7 awarded Famous Question Dec 6 awarded Notable Question Dec 2 awarded Popular Question Nov 30 awarded Popular Question Nov 22 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? Nov 17 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. Nov 15 awarded Notable Question Oct 23 awarded Popular Question Oct 19 awarded Notable Question Oct 7 awarded Notable Question Oct 5 awarded Yearling Oct 1 awarded Notable Question Sep 24 awarded Autobiographer Sep 22 awarded Taxonomist Sep 15 accepted The role of 'arbitrary' in proofs Sep 8 awarded Popular Question