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We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.

Let $K$ be a knot in the $3$-sphere $S^3$, and $\Delta$ a disk in $S^3$ meeting $K$ transversely in the interior. For non-triviality we assume that $|\Delta \cap K|\ge 2$ over all isotopies of $K$ in $S^3-\partial \Delta$. Let $K_{\Delta ,n}$($\subset S^3$) be a knot obtained from $K$ by $n$ twistings along the disk $\Delta$. If the original knot is unknotted in $S^3$, we call $K_{\Delta ,n}$ a . We describe for which pair $(K,\Delta )$ and an integer $n$, the twisted knot $K_{\Delta ,n}$ is a torus knot, a satellite knot or a hyperbolic knot.