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Looking for a book or article on the result linked below. The result tells us that the number of lattice points on a line between points $(a,b)$ and $(c,d)$ is given by $\gcd(a-c,b-d)+1$.

https://math.stackexchange.com/questions/628117/how-to-count-lattice-points-on-a-line

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This result is essentially contained in Apostol's Introduction to Analytic Number Theory. On page 62:

Theorem 3.8 Two lattice points $(a, b)$ and $(m, n)$ are mutually visible if, and only if, $a - m$ and $b - n$ are relatively prime.

The proof of the theorem contains the proof of the counting result you are after.

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  • $\begingroup$ Thanks, @prets! $\endgroup$ Nov 30, 2020 at 20:51

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