You learn to prove why things work, not just that they work.

So ( n+1 ) divides ( n^2+1 ) exactly when ( n+1 ) divides 2. Thus ( n+1 \in {\pm 1, \pm 2} ), giving ( n \in {-3, -2, 0, 1} ). She checked each: all work.

Use the fact that ( I ) is intersection of angle bisectors; then sum of angles in triangle ( BIC ).

Never look at the solution immediately. Spend at least 30–60 minutes grappling with the problem.

If you are stuck after 30–45 minutes, look at the solution. This frustration period is crucial for building neural pathways.