The sign and congruence conjecture for tangent permanents

Let $t_n$ and $t_n'$ be the quantities defined earlier in the paper, and let $\left(\frac{\cdot}{p}\right)$ denote the Legendre symbol. The tangent permanent conjecture.**

(i) For every odd composite integer $n>1$,

$$t_n\equiv0\pmod n.$$

(ii) If $p$ is an odd prime, then

$$\left(\frac2p\right)t_p<0$$

and

$$\left(\frac{-1}p\right)t_p'<0.$$

The claim is motivated by the preceding theorem and remark on these tangent quantities; the supplied text gives no resolution.