What is the remainder when \( { 5 }^{ 50 } \) is divided by 7?
Answer & explanation
Correct answer: option 1
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)