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In this paper we give the absolutely new proof of a conjecture ofR.F.Scott(1881) on the permanent of a Cauchy matrix $\ls \frac{1}{x_i-y_j}\rs_{1 \leqslant i,j \leqslant n},$ where $x_1, ..., x_n$ and $y_1, ..., y_n$are the distinct roots of the polynomials $x^n-1$ and $y^n +1,$ respectively.The simple formula is given for the permanent of the Cauchy matrix $A= \ls\frac{1}{x_i-y_j} \rs_{1 \leqslant i,j \leqslant n},$ where $x_1, ..., x_n$ and$y_1, ..., y_n$ are the distinct roots of the polynomials $x^n+a$ and $y^n +b$,respectively: \begin{gather*} \per (A) =\frac{n}{(b-a)^n}\prod_{k=1}^{n-1}[nb-k(b-a)] = =\begin{cases} %\begin{eqnarray}(-1)^{\frac{n-1}{2}} \cfrac{n}{(b-a)^n}\prod\limits_{k=1}^{\frac{n-1}{2}}[-na-k(b-a)][nb-k(b-a)], \mbox{if $n \equiv 1(\mod 2)$,} \cfrac{n}{2} \cdot \cfrac{n(a+b)}{(b-a)^n}\prod\limits_{k=1}^{\frac{n}{2}-1}[na+k(b-a)][nb+k(a-b)], \mbox{if $n\equiv0(\mod 2)$}. %\end{eqnarray} \end{cases} \end{gather*} from which the correctedformula of R.F.Scott follows instantly. Proof follows from obtained by theauthor a formula for the determinant of an arbitrary of the Hadamard degree $m$of a Cauchy matrix $A$ and Borchard's theorem.

Determinants and permanents of an arbitrary Hadamard degree of a Cauchy matrix and a proof of a generalization of a conjecture of R.F.Scott (1881)