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If $a$, $b$ and $c$ are a Pythagorean triple then prove that $(a^2b^2)^k + (b^2c^2)^k + (c^2a^2)^k$ is divisible for $\dfrac{1}{2}(a^4 + b^4 + c^4)$ for all integer $k \ge 2$.

I cannot think of any way humanly possible to solve the problem. Apologize for that!

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