On the evaluation of R. Chapman's ``evil determinant'' (Q414691)

Let \(p\) be a prime number and let \(\left(\frac \cdot p\right)\) denote the Legrendre symbol. In an unpublished work, R. Chapman conjectured that if \(p\equiv 3\pmod 4\), the determinant of the matrix \(C=\left[\left(\frac{j-i}p\right)\right]\), of order \(\frac{p+1}2\), is \(1\). In this paper, the author proves this result after decomposing \(C\) into a product of several matrices and evaluating the determinant of each such matrices.