# MM Ch3: Arithmetics

## Some problems

### Congruence Arithmetics
$\text{Exercise 17.}$

$$69x \equiv 5 \pmod{23}$$

$69x \pmod{23} \equiv 0x \pmod{23}$ since $69 | 23$. Therefore, this equation has no solution for $x$.

The other way to think:

take a multiple of 23 like 69, then subtract 5 from it. Will you ever get another multiple of 23?