# A miscellaneous algebra question for RMO or Pre-RMO

Question:

If a, b, c are three rational numbers, then prove that

$\frac{1}{(a-b)^{2}} + \frac{1}{(b-c)^{2}} + \frac{1}{(c-a)^{2}}$

is always the square of a rational number.

Solution to be posted soon…

Cheers,

Nalin Pithwa.

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