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Problem of the Day #15: Three Diophantine Equations April 3, 2011

Posted by Billy in : potd , trackback

Find the ordered triple of positive integers $(a,b,c)$ such that \[\begin{align*}a &= \frac{1908}{b(c-b)}-\frac{1908}{b(c+b)} \\ b &= \frac{2600}{a(c-a)}-\frac{2600}{a(c+a)} \\ c &= \frac{686}{a(b-a)}-\frac{686}{a(b+a)} .\end{align*}\]

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