Question

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

Answer 1

so x²- x
= x(x - 1)
so we know every even number can be divided by 2
 if we put any value 
then either of the x or x -1 will be even
that is if we take 2 then 
2(2 -1) is divisible by 2 
if we take 3
3(3 -1)
= 3 (2)
 is divisible by 2  so proved

Answer 2

so given x²- x
= x(x - 1)
so we know any even number can be divided by 2
 if we put any value 
then either of the x or x -1 will be even
that is
if we take 2
then 
2(2 -1) is divisible by 2 
if we take 3
3(3 -1)
= 3 (2) so divisible by 2
if we take 4 
= 4(4-1) so divisible by 2
if we take 5 
= 5(5 - 1)
= 5(4)
 is divisible by 2  so proved