Mistakes give rise to Problems

Algebra Level 4

We know that the denominator can be distributed in a fraction like \[\dfrac{a+b}{c} = \dfrac{a}{c} + \dfrac{b}{c} \]


But you can't do this in \[\dfrac{a}{b+c} = \dfrac{a}{b} + \dfrac{a}{c} \] It will be a mistake if you do it.

But for how many triples \((a,b,c)\) of positive integers is the above (second equation) property true?

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