For the following recursive functions, Prove that am,n = m · n. Here am,n is defined recursively for (m, n) ∈ N × N. am.n = { 0 if m=0 n+am-1,n if m!=0

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For $m=0$ formula is obviously fulfilled. Check it for $m>0$ :

$a_{m,n}=n+a_{m-1,n}=(n+n)+a_{m-2,n}=\ldots=n\cdot m+ a_{0,n}=n\cdot m$

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Question ID: mtid-5-stid-8-sqid-1254-qpid-992