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Prove the following statements using either direct or contrapositive proof. 18. If a,b∈Z,then (a+b)^3 ≡ a^3+b^3...

Prove the following statements using either direct or contrapositive proof.

18. If a,b∈Z,then (a+b)^3 ≡ a^3+b^3 (mod 3).

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Answer #1

Here I'm using divided definition.We know 3|3 then 3 |(3* any nonzero integer).Also a|b and a|c then a|(b+c).Here I'm using (a+b)^3=a^3+3a^2b+3ab^2+b^3.also.proof is below thank you.

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