How to prove with induction [duplicate]

Question

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• How do I write a proof using induction on the length of the input string? 1 answer

So far I have learned how to write proofs by induction and it went fine until I got this recursive problem, which I'm not quite sure how to begin and how to prove that with induction.

            P(2·a,⌊b/2⌋) : b>1 and b is even number
P(a,b):=    P(2·a,⌊b/2⌋)+a : b>1 and b is odd number 
            a :b=1

to prove is for all a,b ∈ N+ -> P(a,b)=a·b

Please don't show me the proof but how to deal with this kind of question.

Thank you