(adsbygoogle = window.adsbygoogle || []).push({}); 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}= 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?

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# Homework Help: Congruence in Z(integers) mod n

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