$a)2020=46^2+0^3-4^3-2^5$ $b)a=3k-4; b=-k; c=k-3; d=0,1,-1$. We get $n=k^3-k^3-9k^2+9k^2+27k-24k+16-27+d^5=3k-11+d^5$. Varying $d=0, 1, -1$ we get all residues $(mod$ $3)$. Hence all integers are cute.

Limerent wrote: $a)2020=46^2+0^3-4^3-2^5$ $b)a=3k-4; b=-k; c=k-3; d=0,1,-1$. We get $n=k^3-k^3-9k^2+9k^2+27k-24k+16-27+d^5=3k-11+d^5$. Varying $d=0, 1, -1$ we get all residues $(mod$ $3)$. Hence all integers are cute. what's the idea of setting a, b, c like that?

tommy2007 wrote: Limerent wrote: $a)2020=46^2+0^3-4^3-2^5$ $b)a=3k-4; b=-k; c=k-3; d=0,1,-1$. We get $n=k^3-k^3-9k^2+9k^2+27k-24k+16-27+d^5=3k-11+d^5$. Varying $d=0, 1, -1$ we get all residues $(mod$ $3)$. Hence all integers are cute. what's the idea of setting a, b, c like that? We want to work with polynomials to run over all integers and we also want to set a b c to kill each other.