How to dollar cost averge with precision

I've seen several dollar cost averaging calculator online, however there is something I usually see missing. How many stocks should you buy if you want your average cost to be a specific value. Usually the calculators will ask how much you bought at each level ang give you the average, but not the other way around (telling you how much to buy to make your average a specific value). For this, I decided to make the calculations on my own.

Here, you can see the mathematical demonstration: mathcha.io/editor/YWvwOi9PFBOhLzm0KmcnrNwvlFMM481HgzmGoo