/sci/ - Science & Math

Stuck on a problem, quite possibly really simple, but I'd like to know if my approach is correct.

The problem is to find every n in <span class="math"> N_0 [/spoiler] so that

<span class="math"> n + 1 \mid n^2 + 1 [/spoiler]

holds true.
Obviously, the answer is <span class="math"> n = \{0, 1\} [/spoiler], but how to get there?

My idea was to prove it by contradiction. Let n be greater 1, then show that the equation is wrong for every n greater than 1, then prove n = 0 and n = 1, and I'm done. Is this the correct approach or did I miss something?

Hello.

I'm searching the solutions for the complex equation

<span class="math"> \frac {2}{z} + z = i[/spoiler], z being an element of the complex numbers and i being the imaginary element.

How do I deal with complex equations in general? Treat them like a normal polynomial?