Proof by Induction: Fixing Errors in Pn | 3-cent and 2-cent Stamps

[PhysicsHelp12]

Let Pn be the statement : any postage of n >= 2 cents can be made of
3-cent and 2-cent stamps. What is wrong with the following proof of
Pn by induction? How can it be fixed without changing the induction
step much?
Base case : 2 = 2 and so P2 is true.
Induction step : Fix some n >=2. Assume that Pk is true for k <= n, we
will prove Pn+1.
Since Pn-1 is true, we know that
n - 1 = a * 2 + b * 3
and hence
n + 1 = (a+1)*2+b*3

 

[CompuChip]

Let n be 2: the argument fails. If you want to talk about n - 1 then n has to be at least 3.