I was wondering if it was possible to quickly find the total amount of lattice points on a circle, given its equation (origin and radius), and I was also a bit confused on how to find a particular point. I don't really have an example, since I only heard of this since my friends younger brother asked us for help, and neither of us had seen this before. Are there standard equations for both finding a specific coordinate point and to find the total amount of points on the circle?
(I suppose to simply it/help my understanding ill just make up a random circle):
$(x-7)^2+(y-3)^2=20$