Okay, That's A Lot Of Integers
Number Theory
Level
5
\[ x+y+z=3 \] \[ x^3+y^3+z^3=3 \] Let \( \displaystyle a \) be the sum of all possible integer values of \( \displaystyle x \).
Let \( \displaystyle b \) be the sum of all possible integer values of \( \displaystyle y \).
Let \( \displaystyle c \) be the sum of all possible integer values of \( \displaystyle z \).
Find \( \displaystyle a+b+c \).
Details and Assumptions:
All the possible values of \(x,y,z\) are to be summed,not only the possible distinct values of \(x,y,z\).For example, if the solutions were \((1,2,3)\) and \((1,2,4)\),then the answer would be \(1+1+2+2+3+4=13\)
by
Adam Phúc Nguyễn