Question
Fri May 27, 2011 By:

show that number x square -x is divisible by 3 or not, for every positive integer x

Expert Reply
Fri May 27, 2011
We have:
x2 - x = x(x - 1)
Now, x and (x - 1) are consecutive integers. We know that the product of two consecutive integers is not always divisible by 3.
For example, 4 x 5 = 20, which is not divisible by 3.
 
Thus, a number of the form x2 - x is not divisible by 3.
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