Exercise 1.

Solve in ${\mathbb{Z}}$ the following equations or systems of equations.

(1)

$7x + 15y = 1$ , with unknown $(x,y)$ ,

(2)

$\left\{ \begin{array}{rccl} x & \equiv & 2 & \mod{3} \\ x & \equiv & 4 & \mod{5} \\ \end{array} \right.$

(3)

$\left\{ \begin{array}{rccl} x & \equiv & 2 & \mod{3} \\ x & \equiv & 4 & \mod{5} \\ x & \equiv & 8 & \mod{7} \\ \end{array} \right.$

Answer 1