Question 3
Find all functions $f:\mathbb Z\to\mathbb Z$ such that, for all integers $x,y,z$,
$$f(x^3+y^3+z^3)=f(x)^3+f(y)^3+f(z)^3.$$
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.
$$f(x^3+y^3+z^3)=f(x)^3+f(y)^3+f(z)^3.$$
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.