/sci/ - Science & Math

[OP !!yzPI6QwWJCg No.5393748]

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?

[Anonymous No.5393761]

n+1=n^2+1

0 = n^2 - n

quadratic formula that bitch dibshit

[Anonymous No.5393770]

n^2 + 1 = (n + 1)(n - 1) + 2

Basically, the '"+ 2" keeps the second term from being a multiple of (n + 1) for n > 1

[Anonymous No.5393806]

>>5393748
if n+1 divides nn+1 then there exists some k st kn+k=nn+1 so (n-k)n+(1-k)=0

so either n-k =0 and k =1 (which means n=k=1)
or
n=0

Defiinition of divides