Find the least non-negative residue of $1729 \pmod{5}$, $1729 \pmod{11}$, and $1729 \pmod{1001}$.
$1729 = 345(5) + 4$ and so $1729 \pmod{5} \equiv 4 \pmod{5}$
$1729 = 157(11) + 2$ and so $1729 \pmod{11} \equiv 2 \pmod{11}$
$1729 = 1(1001) + 728$ and so $1729 \pmod{1001} \equiv 728 \pmod{1001}$