Question 78
Determine the sets $S$ of positive integers satisfying the following two conditions:
a) For any positive integers $a, b, c$, if $ab + bc + ca$ is in $S$, then so are $a + b + c$ and $abc$;
b) The set $S$ contains an integer $N \ge 160$ such that $N - 2$ is not divisible by 4.
a) For any positive integers $a, b, c$, if $ab + bc + ca$ is in $S$, then so are $a + b + c$ and $abc$;
b) The set $S$ contains an integer $N \ge 160$ such that $N - 2$ is not divisible by 4.