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Consider a 1200 digit number Na=aaaa…aaa⏟1200 a’sN_a=\underbrace{aaaa\dots aaa}_{\text{1200 } a\text{'s} }Na=1200 a’saaaa…aaa.
Define φa\varphi_aφa as the number of zeroes in the decimal representation of the quotient obtained when NaN_aNa is divided by 37.
Compute ∑a=19φa\displaystyle\sum_{a=1}^9 \varphi_aa=1∑9φa.
Bonus: Generalize this.
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