Question 100
We will say that the positive integers $m$ and $n$ have property $\mathcal{P}$ if for every divisor $d_1$ of $m$ and every divisor $d_2$ of $n$, the number $d_1 + d_2$ is a prime.
a) Prove that if $m$ and $n$ have property $\mathcal{P}$ and are different, then $m+n$ is odd.
b) Find all the pairs $(m, n)$ of positive integers $m \le n$, having property $\mathcal{P}$.
a) Prove that if $m$ and $n$ have property $\mathcal{P}$ and are different, then $m+n$ is odd.
b) Find all the pairs $(m, n)$ of positive integers $m \le n$, having property $\mathcal{P}$.