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Bézout's identity and Diophantine Equation

  1. Jan 17, 2007 #1
    I am having problems with one exam question.

    Does this diophantine equation have a solution(s)


    as far as I know this is not a linear equation, and what I read online says that Bezout identity only applies for linear diophantine equations.

    The solution says gcd(12,21,33) = 3, 6|3 the above equation has infinitely many solutions. Is that correct? Am I correct to assume then that

    12a+21b+33c+24d = 6 again has infinite solutions aswell?

    How about this equation

    17x+6y +3z =73

    since gcd(17,6,3) = 1 and 73 | 1 this has also infinitely many solutions?
  2. jcsd
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