Let $n \geqslant 2$ be an integer and $x_1, x_2, \ldots, x_n$ be real numbers satisfying \\ \\
(a) $x_j > -1$ for $j = 1, 2, \ldots, n$ and \\ \\
(b) $x_1 + x_2 + \ldots + x_n = n$\\\\
Prove the inequality $$\sum_{j = 1}^{n} \frac{1}{1+x_j} \geqslant \sum_{j = 1}^{n} \frac{x_j}{1+x_j^2}$$ and determine when equality holds.
Školjka 
be an integer and 
be real numbers satisfying 
for 
and 
and determine when equality holds.