Prove that the value of the expression a^2–a is divisible by 2 for any whole value of a.

Answer with explanation:

To prove: is divisible by 2 for any whole value of a.

Consider

Here, a and (a-1) are two consecutive numbers such that,

either of them must be an odd number and an even number.

i.e. a(a-1)= Product of even and an odd number = Even number  [Trivial statement]

⇒ a(a-1) is divisible by 2 [Every even number is divisible by 2.]

⇒   is divisible by 2 for any whole value of a.

Hence proved.

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