Problem 52866. Easy Sequences 36: Hyperbolic Lattice Points

Created by Ramon Villamangca

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The graph, shown below, of the hyperbola: , 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.)
Given the integers a and b, write a function that counts the number of positive lattice points that the hyperbola: , passes through.
NOTE: The trivial point , is not to be included in the count.

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Last Solution submitted on Nov 28, 2025

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GeeTwo on 10 Nov 2022

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.

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Problem 52866. Easy Sequences 36: Hyperbolic Lattice Points

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Problem 52866. Easy Sequences 36: Hyperbolic Lattice Points

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Last 200 Solutions

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Problem Recent Solvers8

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