+ which contradicts the choice of $d$ as the smallest element of $S$. By the division algorithm there are $q,r\in \mathbb{Z}$ with $a = q_1b + r_1$ and $0 \leq r_1 < b$. The pair (x, y) satisfying the above equation is not unique. {\displaystyle d_{1}\cdots d_{n}.} Thus the Euclidean Algorithm terminates. . As this problem illustrates, every integer of the form ax+byax + byax+by is a multiple of ddd. whatever hypothesis on $m$ (commonly, that is $0\le m0$, the definition of $u=v\bmod w$ used in RSA encryption and decryption is that $u\equiv v\pmod w$ and $0\le u