(In reply to
re: Some were discovered.... by Brian Smith)
Interesting patterns I found were the following:
Those that resulted in the natural number 9 would, by multiplying each of a, b, and c by 3 and 9 would give the natural numbers 3 and 1 respectively.
Those that resulted in the natural number 8 would, by multiplying each of a, b, and c by 2, 4, and 8 would give the natural numbers 4, 2 and 1 respectively.
Those that resulted in the natural number 6 would, by multiplying each of a, b, and c by 2, 3, and 6 would give the natural numbers 3, 2 and 1 respectively.
Those that resulted in the natural number 5 would, by multiplying each of a, b, and c by 5 would give the natural number 1.
The following are some of the finds:
a b c (a+b+c)2/(abc)
1 1 1 9
3 3 3 3
9 9 9 1
1 1 2 8
2 2 4 4
4 4 8 2
8 8 16 1
1 1 4 9
3 3 12 3
9 9 36 1
1 2 3 6
2 4 6 3
3 6 9 2
6 12 18 1
1 2 9 8
2 4 18 4
4 8 36 2
8 16 72 1
1 3 8 6
2 6 16 3
3 9 24 2
6 18 48 1
1 4 5 5
5 20 25 1
1 4 25 9
3 12 75 3
9 36 225 1
1 5 9 5
5 25 45 1
1 8 27 6
2 16 54 3
3 24 81 2
6 48 162 1
1 9 20 5
5 45 100 1
1 9 50 8
2 18 100 4
4 36 200 2
8 72 400 1
1 20 49 5
5 100 245 1
1 25 169 9
3 75 507 3
9 225 1521 1
1 27 98 6
2 54 196 3
3 81 294 2
6 162 588 1
1 49 125 5
5 245 625 1
1 50 289 8
2 100 578 4
4 200 1156 2
8 400 2312 1
1 98 363 6
2 196 726 3
3 294 1089 2
6 588 2178 1
2 3 25 6
4 6 50 3
6 9 75 2
12 18 150 1
2 9 121 8
4 18 242 4
8 36 484 2
16 72 968 1
2 25 243 6
4 50 486 3
6 75 729 2
12 150 1458 1
3 8 121 6
6 16 242 3
9 24 363 2
18 48 726 1
|
|
Posted by Dej Mar
on 2007-10-15 13:30:31 |
re(2): Some were discovered....
