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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution further and further ... | Comment 12 of 14 |

   Sloane:  A018782

Smallest k such that circle x^2 + y^2 = k passes through exactly 4n integer points. 

1, 5, 25, 65, 625, 325, 15625, 1105, 4225, 8125, 9765625, 5525, 244140625, 203125, 105625, 27625, 152587890625  etc

Edited on March 1, 2011, 11:25 am
  Posted by Ady TZIDON on 2011-03-01 11:20:45

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