Question

For any positive integer n³-n is divisible by 6

Answer 1

solution :

To prove : any positive integer n cube minus n is divisible by 6

By using euclid's division Lemma,

Let n be any positive integer such that

n = 6q+r , where b= 6 and r is greater than or equal to zero less than 6

=> r=0,1,2,3 ... 5.

If , r=0

n=6q +0=> 6q

n^3 -n (substitute value)

(6q)^3 -6q

216q^3 - 6q

=> 6(36q^2 - q)

Thus , it is divisible by 6

Similarly you can pro for all value of ' r'

Thank you