Remainder-3

By Euler's theorem $19^{92} \pmod{92} \equiv 19^4 \pmod{92}$ . As $\phi(92) = 44$ so $(19^{44})^2 = 19^{88} \pmod{92} \equiv 1 \pmod{92}$ .

Now $19^2 \pmod{92} \equiv 85 \mod{92}$ .

$\therefore 19^4 \pmod{92} \equiv 85^2 \pmod{92} \equiv (-7)^2 \pmod{92} \equiv \boxed{49} \pmod{92}$