What is the remainder when \( { 5 }^{ 49 } \) is divided by 7?

4 3 5 6

5

By Fermat's theorem \( { 5 }^{ 7-1 } \) ≡ 1 (mod 7) \( { 5 }^{ 6 } \) ≡ 1 (mod 7) \( { 5 }^{ 48 } \) ≡ 1 (mod 7) \( { 5 }^{ 49 } \) ≡ 5 (mod 7)