Question

2. Prove that x^2 – x is divisible by 2 for all positive integer x.
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Answer 1

Step-by-step explanation:

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.