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give a whole number

by sanju09 » Fri Jul 30, 2010 4:08 am
Does x³ - x give a whole number when divided by 3?

1. x is a positive integer greater than 1.
2. |x| > 0.

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by selango » Fri Jul 30, 2010 4:23 am
x^3-x/3=?

stmt1,

x>1

x^3-x=x(x^2-1)=x(x+1)(x-1)

=(x-1)x(x+1)

the above represent 3 consecutive integers.Surely this ll be divided by 3.

Suff

stmt2,

|x|>0

x can be 1 or fraction.No info about value of x.

Insuff

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