A circle with $n$ lattice points on it's boundary

Asked Nov 07 '19 at 01:46

Active Nov 07 '19 at 23:54

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Given $n$, is it possible to find a circle in the plane with exactly $n$ lattice points on it?

I misread a problem that asked to show that the above has an affirmative answer with "$n$ lattice points on it" replaced with "$n$ lattice points contained in it", thus motivating the question.

edited Nov 07 '19 at 23:54

asked Nov 07 '19 at 01:46

mtheorylord

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https://www.sciencedirect.com/science/article/pii/S0195669809001012 – Angina Seng Nov 07 '19 at 01:54
The wording is ambiguous; showing AT LEAST $n$ points is easy, showing exactly $n$ might be tricky (if true) – Will Jagy Nov 07 '19 at 02:04
Yeah, I meant the tricky one – mtheorylord Nov 07 '19 at 23:55
you can sort the lattice points based on the distance from the center point. Then just pick radius to be large enough that N nearest points are inside the circle? – tp1 Nov 08 '19 at 00:55

A circle with $n$ lattice points on it's boundary

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