# 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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