The graph, shown below, of the hyperbola: 
, passes through four positive lattice points:
.
, passes through four positive lattice points:.
It can be shown that those 4 points are the only positive lattice points that the above hyperbola touches. (A lattice point is a point 
on the xy-plane where both n and m are integers.)
on the xy-plane where both n and m are integers.)Given the integers a and b, write a function that counts the number of positive lattice points that the hyperbola: 
, passes through.
, passes through.NOTE: The trivial point 
, is not to be included in the count.
, is not to be included in the count.Solution Stats
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The graph labeling is incorrect. The horizontal line is y=2, the vertical is x=4.
Positive lattice points are not defined. From context this appears to be (n,m) where m and n are both positive integers (natural numbers). Note that in the sample case (2,-2) is on the hyberbola but presumably not counted because m==2, or y=2.