A number theory problem by Sravan Chinta

\(Find\quad the\quad number\quad of\quad solutions\quad of\quad (a,b,c)\quad such\quad that\quad \\ \frac { (b+c) }{ a } \quad =\quad \frac { a }{ b } +\frac { a }{ c } \quad \& \quad a,b,c\quad are\quad non-negative\quad integers\\ \& \quad a,b,c<10\)

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