I understand the (i). I did it! I'm smart!

I feel happy when I decompose stuff like 20*15 into 2*10*3*5.

Finding some of them doesn't sound too hard (2020*5 being the first one in base10), but
>(ii) N has at most 2020 decimal digits.
This is a serious downer on my motivation.

>>123463
But you don't like 2²*3*5²?

Counting? Get in the locker dork.

>>123456
Checked.
Stop being such a flipping nerd.

>>123468
I fucked up. It should have been 55, not 5.

whipped this brute-force program up

https://wandbox.org/permlink/QohbrkiJNgwLa8tc

there is a clear pattern once the first N is found, for 2020 that is 4x ones + 2 or more zeros for positive integer x

i wonder if there are any divisors which don't follow that pattern?

>>123892
Here is a proof that the pattern exists (though it doesn't disprove other potential patterns, I am not smart enough for that).

Find a number N that is divisible by X and that consists of d digits: y ones followed by z zeros such that y+z = d

We construct a second number A which is also divisible by X and is guaranteed to be a string of ones and zeros:
A=N*10^y + N

A is divisible by X because it is an integer multiple of N and N is divisible by X: as show by the rewritten equation A = N*(10^y + 1)

A is a string of ones followed by zeros because N*10^y has y ones followed by z zeroes (from N), followed by y more zeroes from 10^y, such that that A is y ones followed by y+z = d zeroes. N is d digits, so there is no overlap between the two parts of A.

>>123893
This is very true and I endorse this math because it... there's numbers and stuff in it.

>>123892
A fraction can be expressed as a repeating decimal where the repeating group of digits is j digits long and starts k digits after the decimal point if and only if it can be expressed as a fraction with a denominator of j "9" digits followed by k "0" digits. We can write 1/2020 as such a fraction with a denominator of j "9" digits followed by k "0" digits if and only if the number with j "1" digits followed by k "0" digits is divisible by 2020. And 1/2020 in decimal form is 0.00(0495).