Question 61
Suppose $a, b, c$ are rational numbers such that
$$
\begin{aligned}
& \left(a^{2}+1\right)^{3}=b+1 \\
& \left(b^{2}+1\right)^{3}=c+1 \\
& \left(c^{2}+1\right)^{3}=a+1
\end{aligned}
$$
Prove that $a=b=c=0$.
$$
\begin{aligned}
& \left(a^{2}+1\right)^{3}=b+1 \\
& \left(b^{2}+1\right)^{3}=c+1 \\
& \left(c^{2}+1\right)^{3}=a+1
\end{aligned}
$$
Prove that $a=b=c=0$.