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