What is the remainder when \( { 5 }^{ 49 } \) is divided by 7?
Answer & explanation
Correct answer: option 3
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)