Statement:For any integer

Proof

Base Case:For

Induction hypothesis:Assume that for some for all

Induction step:Consider . Note that

Using product rule,

By induction hypothesis, and . Therefore, . So the result holds by induction

I know this statement is obviously false, but I can't seem to find anything wrong with the proof that is provided.

I looked through my notes and it looks like every step of the induction process is followed correctly.

Can someone please help me figure out which part is wrong? or give me a hint?