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Special Natural Numbers (Posted on 2007-10-14) Difficulty: 3 of 5
Find all natural numbers which can be written in the form (a+b+c)2/(abc) where a,b,c are also natural numbers.

See The Solution Submitted by Praneeth    
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re(3): Some were discovered.... | Comment 5 of 8 |
(In reply to re(2): Some were discovered.... by Charlie)

 1             1             1             9 
 1             1             2             8
 1             1             4             9
 1             2             3             6
 1             2             9             8
 1             3             8             6
 1             4             5             5
 1             4             25            9
 1             5             9             5
 1             8             27            6
 1             9             20            5
 1             9             50            8
 1             20            49            5
 1             25            169           9
 1             27            98            6
 1             49            125           5
 1             50            289           8
 1             98            363           6
 1             125           324           5
 1             169           1156          9
 1             289           1682          8
 1             324           845           5
 1             363           1352          6
 2             2             4             4
 2             3             25            6
 2             4             6             3
 2             4             18            4
 2             6             16            3
 2             9             121           8
 2             16            54            3
 2             18            100           4
 2             25            243           6
 2             54            196           3
 2             100           578           4
 2             121           1681          8
 2             196           726           3
 3             3             3             3
 3             3             12            3
 3             6             9             2
 3             8             121           6
 3             9             24            2
 3             12            75            3
 3             24            81            2
 3             25            392           6
 3             75            507           3
 3             81            294           2
 3             121           1922          6
 3             294           1089          2
 4             4             8             2
 4             5             81            5
 4             6             50            3
 4             8             36            2
 4             18            242           4
 4             25            841           9
 4             36            200           2
 4             50            486           3
 4             81            1445          5
 4             200           1156          2
 5             9             196           5
 5             20            25            1
 5             25            45            1
 5             45            100           1
 5             81            1849          5
 5             100           245           1
 5             245           625           1
 5             625           1620          1
 6             9             75            2
 6             12            18            1
 6             16            242           3
 6             18            48            1
 6             48            162           1
 6             50            784           3
 6             75            729           2
 6             162           588           1
 8             8             16            1
 8             16            72            1
 8             27            1225          6
 8             36            484           2
 8             72            400           1
 9             9             9             1
 9             9             36            1
 9             20            841           5
 9             24            363           2
 9             36            225           1
 9             75            1176          2
 9             225           1521          1
 12            18            150           1
 12            150           1458          1
 16            72            968           1
 18            48            726           1
 20            25            405           1
 25            45            980           1
Stats:
 1             23
 2             14
 3             13
 4             5
 5             12
 6             12
 8             7
 9             6

  Posted by Charlie on 2007-10-15 14:21:25
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