Why can't we use extended Euclidean method to find the values of x and y?

the equation comes out to be xw+yd=p. if p%gcd(w,d) = 0 => solution exits. From here why we can not use the method of extended euclidean for finding x and y (using the recursive relation of x=y’ y=x’-(a/b)y’)?

What is the requirement of using this method ( modulo inverse method discussed in the lecture)?

hi @sriaryan18_fd3a25b1f1059061 ,
extended euclidean method is used to solve equation of this format : Ax + By = gcd(A,B)
for extended euclidean we need to have gcd(w,d) on RHS right, how would you insure that in case of p?

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