Show that an integer and its cube give the same quotient when divided by 6 .

Dear Student,

Please find below the solution to the asked query :

Suppose a number a is divided by 6 gives a quotient q and remainder r, then we can write,

a=6q+r where  r is an integer such that 

so r takes the values 0,1,2,3,4 and 5.

we see that  cube of each of these numbers leaves a remainder equal to the number itself, when divided by 6.

So,

We see that each of the terms except the last one is a multiple of 6.

In the last term we'll get some quotient say t and a remainder equal to r( as mentioned above)

Hope this would clear your doubt about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards