Question 86
Let $p_1, p_2, \dots, p_{42}$ be 42 pairwise different primes. Prove that the number
$$
\sum_{j=1}^{42} \frac{1}{p_j^2 + 1}
$$
cannot be equal to the reciprocal $\frac{1}{n^2}$ of a perfect square.
$$
\sum_{j=1}^{42} \frac{1}{p_j^2 + 1}
$$
cannot be equal to the reciprocal $\frac{1}{n^2}$ of a perfect square.