The Answer to the Question
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A. For all integers and let is odd. If and are both even than is even too. If and are both odd than is even too. So we have only one of and is odd and .
B. For any integer the number equals to that is the product of three three consecutive natural numbers, one of which is even. In case we have and it is even too.
C. Let's prove that for alll sets and the equality .