Question

the whole numbers xand y are non multiples of 3 and greater than 0. Find the sum of numbers that can be remainders when x^3 + y^3 is divided by 9.

Answer 1

if it is djvided by 9then we can take x as 3 and y as 6

27+216 by 9
27 there fore the sum of the remainder is 27

Answer 2

Remainders are 0, 2 & 7

Step-by-step explanation:

Lets consider the values of x and y, which are non multiples of 3 but greater than zero and  

then find the values of $x^3 + y^3$.

Case -1

• If x = 1 and y = 1 then  

$x^3 + y^3 = 1^3 + 1^3 = 2$

which gives a remainder 2.

Case - 2

• If x = 1 and y = 2 then

$x^3 + y^3 = 1^3 + 2^3 = 9$

which gives a remainder 0.

Case - 3

• If x = 2 and y = 2 then  

$x^3 + y^3 = 8 + 8 = 16$

which gives a remainder 7.

Case - 4  

• If x = 2 and y = 3 then  

$x^3 + y^3 = 8 + 27 = 35$

which is not divisible by 9.

Hence Sum of remainders becomes 0 + 2+ 7 = 9