# Ahaan's polynomial roots

Suppose $u$, $v$, and $w$ are the roots of polynomial $f(x) = x^3 + 20x^2 + 13x + 42,$ and $\frac {1}{u}$, $\frac {1}{v}$, and $\frac {1}{w}$ are the roots of polynomial $g(x) = x^3 + rx^2 + sx + t.$ If $g(1) = \frac {a}{b}$, where $a$ and $b$ are coprime positive integers, what is the value of $a + b$?

This problem is posed by Ahaan Rungta.

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