[Number Theory]
Problem: Let $T=43$. Compute the positive integer $n \neq 17$ for which $\left(\begin{array}{c}T-3 \\ 17\end{array}\right)=\left(\begin{array}{c}T-3 \\ n\end{array}\right)$.

Solution: Using the symmetry property of binomial coefficients, the desired value of $n$ is $T-3-17=T-20$. With $T=43$, the answer is $\mathbf{2 3}$.

Final answer: 23