What is the remainder when \( { 5 }^{ 50 } \) is divided by 7?

4 3 5 6

4

By Fermat's theorem \( { 5 }^{ 7-1 } \) ≡ 1 (mod 7) \( { 5 }^{ 6 } \) ≡ 1 (mod 7) \( { 5 }^{ 48 } \) ≡ 1 (mod 7) \( { 5 }^{ 50 } \) ≡ 25 (mod 7) ≡ 4 (mod 7)