Question

Prove that x2 -x is divisible by 2 for all positive integer x

Answer 1

Answer:

Step-by-step explanation:

Please see the attached explanation

Answer 2

Answer:

To prove : x

2

−x is divisible by 2∀x∈N

x

2

−x=x(x−1)

x and (x−1) are consecutive numbers

So, if x=even (x−1)=odd.

if x=odd (x−1)=even

⇒x(x−1) is always even

⇒x(x−1) is always divisible by 2 for all positive integer.