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).

>>123907
Since you're a math guy, how would you go about proving that 1 + 2 = 3?

>>124030
Why don't you try reposing that question in binary, like a normal person?

>>124031
01001110 01101111

>>124033
I was trying to get you to type out the question of why 01 (a 1 in the singles) and 10 (a 1 in the twos) together make 11 (a 1 in the singles and a 1 in the twos).
I'm not the math guy. I am just pretty sure that simple addition like this is pretty much axiomatic to math. You can't prove it within the framework in a way that makes sense to laypeople.
In other words: We assert that 1+2=3 in order to start doing math.
At best, you could get an analysis of the actual principles underlying the logical construct of math, in a language that can only be understood by people who are math guys themselves.

is math a social construct?

Math uses circular logic

>>124036
The tool of logic is not. It is rigid and objective.
But the things we explore with that tool, depend on what we are interested in.
The search for an odd perfect number, (or for ever higher even perfect numbers) is not reasonable. It's basically just a game.

>>124030
Adding two to a natural number means going to the next number two times. The number after one is two and the number after two is three. We can express this all symbolically with something like

a+0 = a
a+S(b) = S(a+b)
1+1 = 1+S(0) = S(1+0) = S(1) = 2
1+2 = 1+S(1) = S(1+1) = S(2) = 3

but that's what the symbols are saying in plain English.

>>124049
Neat! I don't know what it means, but neat.