# Congruence in Z(integers) mod n

1. Jan 22, 2009

### capsfan828

1. The problem statement, all variables and given/known data

In Z mod 5, compute (a + b)5.

2. Relevant equations

3. The attempt at a solution

Noticing that (a+b)5 = a5+5(a4*b+2*a3*b2+2*a2*b3+a*b4)+b5. Since 5=0 in Z mod 5, it follows that 0(a4*b+2*a3*b2+2*a2*b3+a*b4)=0 and hence (a+b)5=a5+b5.

I am just wondering if it is correct for me to say 5=0 in Z mod 5 and just substitute 0 in for 5?

2. Jan 23, 2009

### Staff: Mentor

$$\equiv$$Sounds reasonable to me. Why don't you test this with a couple of numbers to see if your results are consistent with what you've found?

BTW, instead of saying 5=0 in Z mod 5, you can say 5 $\equiv$ 0 mod 5. That 3-bar equals sign means "is equivalent to".

3. Jan 30, 2009

### capsfan828

thanks for the response, much appreciated