Matt is correct that let k = n is an incorrect substitution because the equation can't be shown to balance. n is already used on the left and I arbitrarily inserted it on the right.

And yes, a single counterexample does disprove a general theorem. However, relying on always being able to quickly find a specific integer that disproves a general theorem is a risky way of doing proofs.

It's not the approach I'd recommend counting on - or studying for - going into a final. What method did he use to find 3? Trial and error is great when it works, but is a horrible feeling in an exam when it doesn't.

What if the next question is "is there any solution set where the equation is true"? Would the answer be "not 3" or would there be more work involved?