Show that 168 cannot be expressed as the sum of the squares of two rational numbers.

Show that 168 cannot be expressed as the sum of the squares of two rational numbers.

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\[13^2=\frac{a^2}{b^2}+\frac{m^2}{n^2}+1\]

\[13^2=\frac{(pm)^2}{(qn)^2}+\frac{m^2}{n^2}+1\]\[13^2=\frac{(pm)^2+(qm)^2}{(qn)^2}+1\]

\[a,b,m,n \in \mathbb{Z}\]

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