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Posers and Puzzles

Posers and Puzzles

  1. 05 Jul '05 12:27 / 1 edit
    Find all pairs of positive integers a and b such that...

    a^2 + b^2 - 7 = ab

    A hint: a^2 - ab - (7-b^2) = 0
  2. 05 Jul '05 12:58
    Originally posted by elopawn
    Find all pairs of positive integers a and b such that...

    a^2 + b^2 - 7 = ab

    A hint: a^2 - ab - (7-b^2) = 0
    I find two pairs: 1 and 3, and 2 and 3

    from a^2 + b^2 -7 =ab also follows that
    a^2 -2ab + b^2 = 7 - ab , or
    (a-b)^2= 7 - ab
    that means 7 >=ab , leaving only (1,1), (1,2), (1,3), (2,2) and (2,3) to check. No heavy calculations necessary for that.
  3. 05 Jul '05 18:41 / 1 edit
    Do they have to be integers?
    EDIT: Stupid me It says so
  4. 07 Jul '05 13:56
    Algebra sucks.
  5. Standard member PBE6
    Bananarama
    07 Jul '05 15:06
    Originally posted by Alpha10
    Algebra sucks.
    And in all the wrong places, too.
  6. 07 Jul '05 15:44 / 1 edit
    Originally posted by Alpha10
    Algebra sucks.
    My Momma always used to say 'Stoopid is as stoopid does'.