# Prove that $(a^2b^2)^k + (b^2c^2)^k + (c^2a^2)^k$ is divisible for $\dfrac{1}{2}(a^4 + b^4 + c^4)$.

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!