For positive integers $a$, $b$, and $c$, what is the value of the product $abc$? \[ \dfrac {1}{a + \dfrac {1}{b + \dfrac {1}{c}}} = \dfrac38 \]

I don't think the $ signs work as math delimiters.  I would be nice if they did.

That looks like a simple continued fraction ("simple" is a technical term meaning the numerators are all 1).



I could go on for hours about continued fractions.  The way we expand a regular fraction as a continued fraction is essentially Euclid's algorithm for the GCD:



So we have a=2, b=1, c=2, a product

abc=4