Let \[S = 5 \times 10 \times 15 \times 20 \times 25 \times 30 \times \ldots \times 1000 \]Let \( x \) be the number of zeros at the end of \( S \). Now,let \[ T = 10 \times 20 \times 30 \times 40\times \ldots \times 1000 \]Then, let \( y \) be the number of zeros at the end of \( T \).\( \frac{x}{y} \) can be expressed as \( \frac{a}{b} \),where \( a \) and \( b \) are positive, coprime integers.Find \( \frac{ab}{31} \).
by
Tan Li Xuan
