What is the remainder when \( { 4 }^{ 37 } \) is divided by 7?
Answer & explanation
Correct answer: option 4
By Fermat's theorem
\( { 4 }^{ 7-1 } \) ≡ 1 (mod 7)
\( { 4 }^{ 6 } \) ≡ 1 (mod 7)
\( { 4 }^{ 36 } \) ≡ 1 (mod 7)
\( { 4 }^{ 37 } \) ≡ 4 (mod 7)