Mistakes Give Rise to Problems

Algebra Level 3

We know \[a^{m+n}=a^m \times a^n\] But there are some students who claim that \[a^{m+n}=a^m+a^n\] which is obviously incorrect. However, it is true for some triplets of integers, \((a,m,n)\). If \(a\in[0,10]\) and \(m,n\in[1,10]\), then find the number of possible triplets for which \(a^{m+n}=a^m+a^n\).

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