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
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2 comments:

  1. ClaudioDecember 3, 2010 at 12:21 PM

    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

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  2. BenVitaleDecember 4, 2010 at 11:25 AM

    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

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