What is the remainder when \( { 4 }^{ 37 } \) is divided by 7?

1 2 3 4

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)