What are the numbers divisible by 9001?

9001, 18002, 27003, 36004, 45005, 54006, 63007, 72008, 81009, 90010, 99011

There is a total of 11 numbers (up to 100000) that are divisible by 9001.
The sum of these numbers is 594066.
The arithmetic mean of these numbers is 54006.

How to find the numbers divisible by 9001?

Finding all the numbers that can be divided by 9001 is essentially the same as searching for the multiples of 9001: if a number N is a multiple of 9001, then 9001 is a divisor of N.

Indeed, if we assume that N is a multiple of 9001, this means there exists an integer k such that:

$k \times 9001 = N$

Conversely, the result of N divided by 9001 is this same integer k (without any remainder):

$k = \frac{N}{9001}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 9001 (we can keep multiplying it by increasingly larger integers, without ever reaching the end).

However, in this instance, we've chosen to set an arbitrary limit (specifically, the multiples of 9001 less than 100000):

1 × 9001 = 9001
2 × 9001 = 18002
3 × 9001 = 27003
...
10 × 9001 = 90010
11 × 9001 = 99011