A line passes through $A(1,1)$ and $B(100,1000)$. How many other points with integer coordinates are on the li

Question

A line passes through $A(1,1)$ and $B(100,1000)$. How many other points with integer coordinates are on the line and strictly between $A$ and $B$?

GPT-5 mini · Answer

Vector AB = (99, 999) = 9(11, 111), so gcd(99,999)=9.  
Number of lattice points on the segment AB is gcd(99,999)+1 = 10, hence strictly between A and B there are 10−2 = 8 points.

A line passes through $A(1,1)$ and $B(100,1000)$. How many other points with integer coordinates are on the line and strictly between $A$ and $B$?

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