1,466 reputation
21745
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location Valdosta, ga
age 22
visits member for 2 years, 2 months
seen 22 hours ago

I am just a man who has an insatiable desire for knowledge.

"For the rest, brethren, whatever is true, whatever is worthy of reverence and is honorable and seemly, whatever is just, whatever is pure, whatever is lovely and lovable, whatever is kind and winsome and gracious, if there is any virtue and excellence, if there is anything worthy of praise, think on and weigh and take account of these things [fix your minds on them]."~ Philippians 4:8


22h
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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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accepted The role of 'arbitrary' in proofs
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