I am playing this cool game called Territory Idle. In this game, two types of buildings can earn resources. Some earn a resource for each worker while others add one per worker of the resource.
Here is an example: I have two temples, each with 70 workers. Each temple worker earns me 1 faith point plus as many points as there are workers in the cathedral.
I would like to know what combinations of $x$ (the total number of temple workers) and $y$ (the number of cathedral workers) amount to a rate of earning that is a multiple of 1000. For instance, with $140$ temple workers, $49$ cathedral workers give $+7000$ faith per second.
So far I have $x(y+1) \pmod{1000} = 0$
I don't even know if I'm on the right track.
Update:
Using @InterstellarProbe's answer I was able to visualize the solutions, which suits my needs.
$1000 = 2^3 5^3$ so between $x$ and $y+1$, you need those prime factors. Thus, you can have any of the following:
$$\begin{array}{c}(x,y) \\ \hline (m,1000n-1) \\ (2m,500n-1) \\ (4m,250n-1) \\ (5m,200n-1) \\ (8m,125n-1) \\ (10m,100n-1) \\ (20m,50n-1) \\ (25m,40n-1) \\ (40m,25n-1) \\ (50m,20n-1) \\ (100m,10n-1) \\ (125m,8n-1) \\ (200m,5n-1) \\ (250m,4n-1) \\ (500m,2n-1) \\ (1000m,n-1)\end{array}$$
This works for any positive integers $m,n$. Just pick a pair, and plug in any positive integer $m,n$, and it will give you a valid $(x,y)$.