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Math Help - Diophantine Equation? Or something?

  1. #1
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    Diophantine Equation? Or something?



    Lost. Sorry.
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  2. #2
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    4x^2 - y^2 = (2x + y)(2x - y) = 480.

    Now list all the pairs of numbers that can multiply to 480:

    (480, 1); (240, 2); (160, 3); (120, 4); (96, 5); (80, 6);

    (60, 8); (48, 10); (40, 12); (32, 15); (30, 16); (24, 20)

    The pairs with one odd number and one even number will result in y not being an integer, so you can throw those out. Also, the pairs such that the sum of the numbers is not divisible by 4 will result in x not being an integer, so you can throw those out.

    1. 2x + y = 120

    2x - y = 4

    4x = 124

    x = 31, y = 58 is a solution.

    2. 2x + y = 60

    2x - y = 8

    4x = 68

    x = 17, y = 26 is a solution.

    3. 2x + y = 40

    2x - y = 12

    4x = 52

    x = 13, y = 14 is a solution.

    4. 2x + y = 24

    2x - y = 20

    4x = 44

    x = 11, y = 2 is a solution.

    Hence the solutions are (31, 58); (17, 26); (13, 14); (11, 2).
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  3. #3
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    Very detailed. Thank you muchly.
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