Very interesting, Alon Amit! (Can I please have some anonymized network data?) Suppose f : Z^3 —> Z via f(x,y,z) = x^3 + y^3 + z^3. Then f can evidently take some very large triples to very small integers. Question: ----- Given an integer N in Z: What is the asymptotic behavior of the set S_3(N) = ((x,y,z) in Z^3 | x^3 + y^3 + z^3 = N} ??? Meaning above all: What is the asymptotic behavior of the monotone function #_3(N): Z+ —> Z>=0 where #_3(N)(t) denotes the number card({(x,y,z) in Z^3 | x^3 + y^3 + z^3 = N —and— x^2 + y^2 + z^2 <= t} And same for other polynomials. —Dan ----- James Buddenhagen writes: ----- 33=8866128975287528^3+(-8778405442862239)^3+(-2736111468807040)^3 found by Timothy Browning communicated on Quora by Alon Amit -----