The powers of 333 modulo 777 cycle with period 666: 31≡3,32≡2,33≡6,34≡4,35≡5,36≡1(mod7)3^1 \equiv 3, \quad 3^2 \equiv 2, \quad 3^3 \equiv 6, \quad 3^4 \equiv 4, \quad 3^5 \equiv 5, \quad 3^6 \equiv 1 \pmod{7}31≡3,32≡2,33≡6,34≡4,35≡5,36≡1(mod7) What is 317(mod7)3^{17} \pmod{7}317(mod7)?
333
444
555
666