It is currently not known whether odd perfect numbers (numbers with the property $\sigma(n)=2n$, where $\sigma(n)$ is the sum of divisors of $n$, including $1$ and $n$) exist.
But suppose, a perfect odd number exists.
Do we then know whether there are infinite many perfect odd numbers ?
This could be possible because various necessary conditions are known for an odd number to be perfect. Perhaps they allow to construct arbitary many perfect odd numbers, supposing that an odd perfect number exists.