AT-OEMO-REG 2011 Problem 1

Let $p_1, p_2, \ldots, p_{42}$ be $42$ pairwise distinct prime numbers. Show that the sum $$\sum_{j=1}^{42}\frac{1}{p_j^2+1}$$ is not a unit fraction $\frac{1}{n^2}$ of some integer square number.