## Wednesday, December 1, 2010

### Looking for postive integers such that

The positive integers are the numbers

Here I'm interested to find all positive integers which can be written in the form

(1) (a + b + c)^2 /(abc)
(2) (a + b - c)^2 /(abc)
(3) (a - b + c)^2 /(abc)
(4) (a - b - c)^2 /(abc)

where a, b, c are positive integers

1. I found this:
1 + 29 + 6 = 36
36^2 = 1296
1296 / 1296 = 1

1 + 45 + 8 = 54
54^2 = 2916
2916 / 1458 = 2

1 + 93 - 6 = 88
88^2 = 7744
7744 / 1936 = 4

2 + 8 + 83 = 93
93^2 = 8649
8649 / 2883 = 3

3 + 3 - 64 = -58
-58^2 = 3364
3364 / 3364 = 1

3 - 9 + 69 = 63
63^2 = 3969
3969 / 3969 = 1

3 + 87 - 2 = 88
88^2 = 7744
7744 / 3872 = 2

5 + 77 - 6 = 76
76^2 = 5776
5776 / 5776 = 1

6 + 72 + 4 = 82
82^2 = 6724
6724 / 6724 = 1

7 + 3 - 96 = -86
-86^2 = 7396
7396 / 7396 = 1

8 + 2 + 81 = 91
91^2 = 8281
8281 / 8281 = 1

82 + 8 + 1 = 91
91^2 = 8281
8281 / 8281 = 1

2. If you try the small numbers from 1 to 9 in (1) (a + b + c)^2 /(abc) you notice that 7 cannot be used. We get only 1,2,3,4,5,6,8,9.
I'm going to try with other numbers,i.e. from 10 to 100.
And try with eq. #2, #3 and #4