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Math Help - Give one solution

  1. #1
    Super Member dhiab's Avatar
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    Give one solution

    Find one solution for equation :  x^4 + y^\alpha = z^4
    Where x,y,z,\alpha are positive integers.
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  2. #2
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    Quote Originally Posted by dhiab View Post
    Find one solution for equation :  x^4 + y^\alpha = z^4
    Where x,y,z,\alpha are positive integers.
    By inspection, wouldn't (x,y,z,\alpha ) = (2, 65, 3, 1) work?
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  3. #3
    Super Member dhiab's Avatar
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    Quote Originally Posted by QM deFuturo View Post
    By inspection, wouldn't (x,y,z,\alpha ) = (2, 65, 3, 1) work?
    Hello Thank you are you the details?
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    Quote Originally Posted by dhiab View Post
    Hello Thank you are you the details?
    "By inspection" means you take a look and try to guess values that will work. In this case I realized I could use y^\alpha as a "wildcard", by setting alpha to 1, I could then set y to whatever I needed to make it work with the values I chose for x and z. Then I tried a few values of x and z that might work, by rewriting

    y^1 = z^4 - x^4. Since the solution set is positive integers, z > x, so I chose z = 3, x = 2.
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