What is the remainder when \( { 11 }^{ 14 } \) is divided by 7?
Answer & explanation
Correct answer: option 4
By Fermat's theorem
\( { 11 }^{ 7-1 } \) ≡ 1 (mod 7)
\( { 11 }^{ 6 } \) ≡ 1 (mod 7)
\( { 11 }^{ 12 } \) ≡ 1 (mod 7)
\( { 11 }^{ 14 } \) ≡ 121 (mod 7) ≡2 (mod 7)