What is the conjecture

For any two positive coprime integer numbers $a \neq u$ the eighth degree polynomial

$$ P_{au}(t) = t^8 + 6(u^2-a^2)t^6 + (a^4-4a^2u^2+u^4)t^4 - 6a^2u^2(u^2-a^2)t^2 + u^4a^4 $$

is irreducible over the ring of integers $\mathbb Z$.

• https://en.wikipedia.org/wiki/Euler_brick#Cuboid_conjectures

Prerequisites needed

AMS categories

• ams-12

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• I plan on adding this conjecture to the repository
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