Congruence in Z(integers) mod n

[capsfan828]

Homework Statement

In Z mod 5, compute (a + b)⁵.

Homework Equations

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?

 

[Mark44]

$$\equiv$$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".

 

[capsfan828]

thanks for the response, much appreciated