A Fascinating problem

$\begin{aligned} \text{We have ,}\\ \phi(9)&=9(1-\dfrac{1}{3})=6, \hspace{4mm}\color{#3D99F6}\phi(n) \text{ is the Euler totient function.}\\ \text{Since } 4 &\text{ and } 9 \text{ are coprime by Euler's theorem we have,}\\ 4^{\phi(9)}&\equiv1\pmod{9}\\ 4^6&\equiv 1\pmod{9}\\ \implies 4^{18}-1 &\equiv0 \pmod {9}\\\\ \implies \text{Sum of digits of }&\overline{ 687194a6735} \text{ is divisible by }9. \\ \implies 56+a &\equiv 0\pmod{9}\\ \implies a&=\color{#EC7300}\boxed{\color{#333333}7}\end{aligned}$