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Examples 1.1.5(a):

Prove that when two even integers are multiplied, the result is an even integer, and when two odd integers are multiplied, the result is an odd integer.
To prove this we first need to know what exactly an even and odd integer is: Now that we have a precise definition, the actual proof is easy: Take x and y two even numbers. Then Multiplying these numbers together we get where k = 2nm. Hence, xy is again even.

If x and y are two odd numbers, then

Multiplying these numbers together we get where k = 2nm + n + m. Hence, xy is again odd.
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