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## Homework Statement

In Z mod 5, compute (a + b)

^{5}.

## Homework Equations

## The Attempt at a Solution

Noticing that (a+b)

^{5}= a

^{5}+5(a

^{4}*b+2*a

^{3}*b

^{2}+2*a

^{2}*b

^{3}+a*b

^{4})+b

^{5}. Since 5=0 in Z mod 5, it follows that 0(a

^{4}*b+2*a

^{3}*b

^{2}+2*a

^{2}*b

^{3}+a*b

^{4})=0 and hence (a+b)

^{5}=a

^{5}+b

^{5}.

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?