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 Integer points on circles. (Posted on 2011-02-28)
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.

 Submitted by Jer Rating: 3.5000 (2 votes) Solution: (Hide) r=1 has 4. (1,0) etc. r=√5 has 8. (2,1) (1,2) etc. r=5 has 12. (5,0) (4,3) (3,4) etc. r=√65 has 16. (8,1) (1,8) (7,4) (4,7) etc. r=65 has 20. (65,0) (60,25) (25,60) (52,39) (39,52) etc. See http://oeis.org/A071383 for more terms.

 Subject Author Date re: OEIS sequence, NOT THIS ONE Ady TZIDON 2011-03-01 16:37:47 OEIS sequence Brian Smith 2011-03-01 11:26:35 further and further ... Ady TZIDON 2011-03-01 11:20:45 re(2): n = 2 Steve Herman 2011-03-01 11:08:26 re: n = 3 (spoiler), difficulty d2? Ady TZIDON 2011-03-01 09:11:08 re: n = 2 Ady TZIDON 2011-03-01 09:09:29 n = 4 + full solution (spoiler) Steve Herman 2011-03-01 03:26:31 n = 5 (spoiler) Steve Herman 2011-03-01 03:07:21 N=5 Brian Smith 2011-02-28 21:32:14 A symmetry argument Steve Herman 2011-02-28 18:03:38 n = 3 (spoiler), difficulty d2? Steve Herman 2011-02-28 17:57:40 n = 2 Steve Herman 2011-02-28 17:50:01 re: 1st four --d1 Steve Herman 2011-02-28 17:48:17 1st four --d1 Ady TZIDON 2011-02-28 13:50:12

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