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.


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.

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