Mistakes Give Rise to Problems

Algebra Level 3

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

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