What is the remainder when \( { 3 }^{ 19 } \) is divided by 7?
Answer & explanation
Correct answer: option 1
By Fermat's theorem
\( { 3 }^{ 7-1 } \) ≡ 1 (mod 7)
\( { 3 }^{ 6 } \) ≡ 1 (mod 7)
\( { 3 }^{ 18 } \) ≡ 1 (mod 7)
\( { 3 }^{ 19 } \) ≡ 3 (mod 7)