1200 followers problem!
Number Theory
Level
5
Consider a 1200 digit number \(N_a=\underbrace{aaaa\dots aaa}_{\text{1200 } a\text{'s} }\).
Define \(\varphi_a\) as the number of zeroes in the decimal representation of the quotient obtained when \(N_a\) is divided by 37.
Compute \(\displaystyle\sum_{a=1}^9 \varphi_a\).
Bonus: Generalize this.
by
Nihar Mahajan