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Diophantine equation and squares

  1. Apr 3, 2015 #1
    The Diophantine equation below,

    $$ x_0^{2} - (x_1^{2}+x_2^{2}+x_3^{2}+x_4^{2}+x_5^{2}+x_6^{2}+x_7^{2}+x_8^{2})=1$$

    1. Does above equation have any specific name?
    2. What are the solutions(a formula)??
    3. in the case,$$x_8^{2}=0$$ , does anything special happen??
    4. What is the general way to approach/solve these kind of equation??

    Any kind of comment would help!!
    Last edited: Apr 3, 2015
  2. jcsd
  3. Apr 5, 2015 #2


    Staff: Mentor

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