Forgive me if this is wrong. I haven't done stat in a year, but comment if you need clarification!
Rewrite this equation
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Consider expression First, you can factor it:
Since x is integer number, then you can see that x-1 is previous integer number (x-1 is 1 unit smaller than x).
Therefore, x-1 and x are two consecutive integers. When you have two consecutive integers, one of them is always even and one is always odd. Multiplying even integer number by odd integer number you always get even integer number.
Thus, is always even.