Could you help me with this problem?
The sum of the positive factors of some positive integer $N$ is $96$. The sum of the positive factors of $N-1$ is $N$. What is the sum of the positive factors of $N+1$?
Note: As $N-1 + 1 = N$ , we have that $N-1$ is a prime number. $42=2*3*7$ seems to be a solution, but I'm not sure if it's unique.
Thanks for any help!
You've already deduced that $N-1$ is prime. Next it's worth noting that the sum of all positive factors of $N$ is at least as big as $N$ itself, so $N\leq96$. This leaves only finitely many cases to check, which is quite doable.
The solution is not unique; the sum of the positive factors of $N+1$ could be either $44$ or $104$. Or $42$ if you allow $N$ to be negative.