オリジナル
a+b+c,a3+b3+c3-3abc

wolframalphaで

(1)

もしかしたら、次の入力がまちがっているかもしれません。

(2)
省略

(3)

整数解の数18
18÷(321)=3

{
{a == -2, b == 2, c == 3}, 
{a == -2, b == 3, c == 2}, 
{a == -1, b == 0, c == 4}, 
{a == -1, b == 4, c == 0}, 
{a == 0, b == -1, c == 4}, 
{a == 0, b == 4, c == -1}, 
{a == 2, b == -2, c == 3}, 
{a == 2, b == 3, c == -2}, 
{a == 3, b == -2, c == 2}, 
{a == 3, b == 2, c == -2}, 
{a == 4, b == -1, c == 0}, 
{a == 4, b == 0, c == -1}, 
{a == 6, b == 7, c == 8}, 
{a == 6, b == 8, c == 7}, 
{a == 7, b == 6, c == 8}, 
{a == 7, b == 8, c == 6}, 
{a == 8, b == 6, c == 7}, 
{a == 8, b == 7, c == 6}
}

sympyで

(勉強中)

参考