SOLUTION: Prove that x^2 -x ,is divisible by 2

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Question 1068303: Prove that x^2 -x ,is divisible by 2
Found 2 solutions by KMST, rothauserc:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If x%3E1 is a positive integer,
x%5E2-x=x%28x-1%29 is the product of two consecutive integers,
so one of those integers must be even,
so the product must be even.
Either x=2n is even,
with n being a positive integer,
and x%28x-1%29=2n%28x-1%29 is a multiple of 2,
or dividing x by 2 there is a quotient q and a remainder {1} .
In that case, x=2q%2B1 , x-1=2q ,
and x%28x-1%29=%282q%2B1%29%2A2q is a multiple of 2.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - x = x * (x - 1)
:
1) if x is even then we have the product of an even and an odd number which is even
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2) if x is odd then we have the product of an odd number and an even number which is even
:
In both cases(1 and 2) we have an even number which is divisible by 2
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