Question 2
Prove that the system of equations $$\begin{aligned} x^6 + x^3 + x^3y + y &= 147^{157} \\ x^3 + x^3y + y^2 + y + z^9 &= 157^{147} \end{aligned}$$ has no integer solutions.
Proposed by Răzvan Gelca (credited in the supplied source).
Proposed by Răzvan Gelca (credited in the supplied source).