(a) Find \(r\) with \(0 \leq r \leq 10\) such that \(7^{137} \equiv r \bmod 11\).

(b) Find \(r\) with \(0 \leq r<645\) such that \(2^{81} \equiv r \bmod 645\).

(c) Find the last two digits of \(3^{124}\) (when expressed in decimal notation).

(d) Show that there is a multiple of 21 which has 241 as its last three digits.