Answer with explanation:
To prove: [tex]a^2-a[/tex] is divisible by 2 for any whole value of a.
Consider [tex]a^2-a=a(a-1) \ \ \ \ [\text{ Taking 'a' out as common }][/tex]
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.]
⇒ [tex]a^2-a[/tex] is divisible by 2 for any whole value of a.
Hence proved.
