2.2 Congruences

Why cannot we cancel the $2$'s in the equation $8\cdot 2 \equiv 3 \cdot 2 (\text{mod } 10)$ to $8 \equiv 3 (\text{mod } 10)$?

Exercise 1

  2 is a prime number 2 is even 2 has common factors with 10 10 is not a power of 2 We CAN cancel the 2 2 has common factors with 10 

If $k$ and $n$ are _____, then $k$ has a multiplicative inverse in the equation $a\cdot k \equiv b\cdot k (\text{mod } n)$.

Exercise 2

  collinear of different parity relatively prime invertible irreducible distinct relatively prime