# Math Help - mod

1. ## mod

a "is congruent to b" (mod 2) if and only if a and b have the same parity.

Any advice?

2. Originally Posted by jzellt
a "is congruent to b" (mod 2) if and only if a and b have the same parity.

Any advice?
Here is some advice. a is congruent to b (mod 2) means that 2 divides their difference.

so, $2 \mid (a - b)$ or in other words $a - b = 2k$ for some integer $k$

Can you continue?

3. I've gotten that far, but Im not sure what it means that a and b have the same parity.

4. Originally Posted by jzellt
a "is congruent to b" (mod 2) if and only if a and b have the same parity.

Any advice?
$a\equiv b(\bmod 2)$ if and only if when we write $a=2q_1+r_1$ and $b=2q_2+r_2$ in the form of the division algorithm we have $r_1=r_2$.

5. Originally Posted by jzellt
I've gotten that far, but Im not sure what it means that a and b have the same parity.
same parity means they are both odd or they are both even