We know the theorem of linear diophantine equation from Bezout's identity that the solution is in ordered pair form:

$\left(x + m \dfrac{b}{\text{gcd}(a,b)}\,,\,y-m \dfrac{a}{\text{gcd}(a,b)}\right)$

For all integers $m$

Then, what is the general integer solutions for a linear diophantine equation with 3 or more than 3 variables?

  • $\begingroup$ Suggest you state what equation your pairs are a solution of. $\endgroup$ – coffeemath May 2 at 0:32
  • $\begingroup$ Says $ax+by+cz=d$ $\endgroup$ – user516076 May 2 at 23:23
  • $\begingroup$ Yes, but better to put that in question, say above solution. $\endgroup$ – coffeemath May 3 at 2:03
  • $\begingroup$ Anyway i got the answer already. Thanks $\endgroup$ – user516076 May 3 at 22:51

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