Arithmetic On Even and Odd Numbers
The following laws can be verified using the properties of divisibility. They are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. As with ordinary arithmetic, multiplication and addition are commutative and associative, and multiplication is distributive over addition. However, subtraction in parity is identical to addition, so subtraction also possesses these properties (which are absent from ordinary arithmetic).
Read more about this topic: Parity (mathematics)
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