1200 followers problem!

Consider a 1200 digit number Na=aaaaaaa1200 a’sN_a=\underbrace{aaaa\dots aaa}_{\text{1200 } a\text{'s} }.

Define φa\varphi_a as the number of zeroes in the decimal representation of the quotient obtained when NaN_a is divided by 37.

Compute a=19φa\displaystyle\sum_{a=1}^9 \varphi_a.


Bonus: Generalize this.

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