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Math Help - solve in N

  1. #1
    Super Member dhiab's Avatar
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    solve in N

    x , y , z is primes numbers
    solve :
    x^3=x^2+y^2+z^2
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: solve in N

    One obvious solution: x=y=z=3.
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  3. #3
    Super Member dhiab's Avatar
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    Re: solve in N

    thak you
    but how?
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  4. #4
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    Re: solve in N

    Quote Originally Posted by dhiab View Post
    x , y , z is primes numbers
    solve :
    x^3=x^2+y^2+z^2
    Use congruence mod 3.
    [1] x = 0 (mod 3) then x = 3 and y^2 + z^2 = 18 which implies y = z = 3
    [2] x = 1 (mod 3) then ......
    [3] x = 2 (mod 3) then ......
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