My task requires some euclidian work beforehand
gcd(4386, 89744) = 4386 x + 89744 y
I've confirmed that
gcd(4386, 89744) = 2
Does that mean that
4386 x + 89744 y = 2?
I ask because this format is the basis of a youtube tutorial.
2026-03-25 20:34:15.1774470855
Linear diophantic equation
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It does clearly not mean that for any $x,y$ : $4386 x + 89744 y = 2$ if it's what you meant. What is true is that the equation $4386 x + 89744 y = 2$ has an integer solution, that is: there are $x,y$ so that $4386 x + 89744 y = 2$ (namely $x = 22569, y = -1103$).
In general: If you have gcd(a,b)=c then the equation $ax +by = c$ has an integer solution.