I have solved such an equation using the euclidean algorithm. However, unlike other methods, this gives one solution. Is this just one solution or the only solution.
Help is much appreciated.
Thank you
2026-03-27 18:34:40.1774636480
If the euclidean algorithm is used to solve an equation ( i.e., $ax = b \mod(z)$) is the solution unique?
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No. For instance, if you consider the equation $$ 3x \equiv 6 \pmod{9},$$ then there are the three incongruent solutions $2, 5, 8 \pmod 9$. But the Euclidean Algorithm will only ever give you one congruence class of solutions. However, if $\gcd(a,z) = 1$ in $ax \equiv b \pmod z$, then the solution from the Euclidean Algorithm is the only solution.