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Integer points on circles. (Posted on 2011-02-28) Difficulty: 3 of 5
If a circle is centered on the origin and has radius r, it may pass through some points with integer coordinates. In fact, by symmetry, this will be a multiple of 4.

Find the smallest radius that will pass through 4n integer points where n=1,2,3,4,5.

Feel free to go further.

See The Solution Submitted by Jer    
Rating: 3.5000 (2 votes)

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Some Thoughts N=5 | Comment 6 of 14 |

One solution for N=5 will have a radius of 65 units, passing through (0,65), (25,60), (60,25), (39,52), (52,39), and 15 other points located symmetrically in the second, third and fourth quadrants.

I got this solution by scaling a 3-4-5 and a 5-12-13 triangle until they both had a hypotenuse of 65.


  Posted by Brian Smith on 2011-02-28 21:32:14
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