Question

prove that a square minus x ID dirigible by 2 from all positive integer x​

Answer 1

Step-by-step explanation:

Well, the proof is exceedingly simple. Consider the fact that x is a positive integer. Now, consider the result x²-x which is essentially x(x-1) 

Consider this product of x and (x-1). Now, for any positive integer x, x-1 is the number immediately lower than the number. 

There are two cases:

Case 1: x is even, so x can be modelled as a generic number 2n, where n is a positive integer.

Now,x(x-1)= 2n(2n-1)

Clearly this product is divisible by two. 

Case 2: x is odd, so x can be written as the generic number 2n+1 where n is any integer ≥0

Now, x(x-1)= (2n+1)(2n+1-1)= (2n+1)(2n)

Clearly, this is again divisible by two.

Hence, it is safe to generalise that the term x²-x is divisible by 2 for any positive integer x.