* even × even = even;
* even × odd = even;
* odd × odd = odd.

By construction in the previous section, the structure ({even, odd}, +, ×) is in fact the field with two elements.

Division

The division of two whole numbers does not necessarily result in a whole number. For example, 1 divided by 4 equals 1/4, which is neither even nor odd, since the concepts of even and odd apply only to integers. But when the quotient is an integer, it

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