Hi, maybe some of you guys know Project Euler already, if not, please follow the link and read a bit about it. It is a collection of interesting mathematical problems. This is my take on the first problem:

Find the sum of all the multiples of 3 or 5 below 1000

While this is a one line problem in python:

print(sum([0 if i % 3 and i % 5 else i in range(1000)]))

solving this analytically is challenging.

This is how far I got:

wherefore $i^{k_i} \cdot j^{k_j} < W$ is always valid.

As $\log$ is a strict monotonic function, we can change this to

So the needed value can be defined as:

Now, apply this summation formula:

which results in

well… and this is how far I got. I could reformulate it to:

with $ \{ \} $ as the frac function. I have no idea how to proceed from here. :(

So if you see an error or have an idea, please write me!

I also found a different solution here: Muvik.de but I really like to know how to solve my problem!