Odd integer

An odd integer $n$ is an integer which is not a multiple of $2$ (or equivalently one more than a multiple of $2$). The odd integers are $\ldots, -5, -3, -1, 1, 3, 5, \ldots.$ Every odd integer can be written in the form $2k + 1$ for some unique other integer $k$.

The product of any two odd integers is odd, but the sum and difference of any two odd integers are even.

The sum and difference of an even integer and odd integer are odd. Besides $2,$ all prime numbers are odd.

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