I am having problems with one exam question. Does this diophantine equation have a solution(s) 12a+21b+33c=6 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?