What is the remainder when \( { 2 }^{ 15 } \) is divided by 7?
Answer & explanation
Correct answer: option 4
By Fermat's theorem
\( { 2 }^{ 7-1 } \) ≡ 1 (mod 7)
\( { 3 }^{ 6 } \) ≡ 1 (mod 7)
\( { 3 }^{ 12 } \) ≡ 1 (mod 7)
\( { 3 }^{ 15 } \) ≡ 8 (mod 7)