Exercise 111.31.1. Consider the affine curve $X$ given by the equation $t^2 = s^5 + 8$ in $\mathbf{C}^2$ with coordinates $s, t$. Let $x \in X$ be the point with coordinates $(1, 3)$. Let $U = X \setminus \{ x\} $. Prove that there is a regular function on $U$ which is not the restriction of a regular function on $\mathbf{C}^2$, i.e., is not the restriction of a polynomial in $s$ and $t$ to $U$.

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