It is interesting whether there exist three integers a,b,c for the equation a3+b3+c3=y, where y is a given integer. This problem is called the sum of three cubes problem. The answer is YES for y=3 or y=2. For example, 13+13+13=43+43+(5)3=313+13+03=12149283+34802053+(3528875)3=2. In September 2019 , the number y=42 was solved. This success completes the solution of each number between 1 and 100 . It was also known that there is no solution for some values of y (described in subproblem b) before y=42 was solved. Prove the following: (a) The cube of any integer modulo 9 is 1,1, or 0 . (b) If y modulo 9 is 4 or 5 , then there is no solution for y in the sum of three cubes