What is the remainder when \( { 3 }^{ 30 } \) is divided by 7?
Answer & explanation
Correct answer: option 2
By Fermat's theorem
\( { 3 }^{ 7-1 } \)≡ 1 (mod 7)
\( { 3 }^{ 6 } \) ≡ 1 (mod 7)
\( { 3 }^{ 30 } \) ≡ 1 (mod 7)
What is the remainder when \( { 3 }^{ 30 } \) is divided by 7?
Correct answer: option 2
By Fermat's theorem
\( { 3 }^{ 7-1 } \)≡ 1 (mod 7)
\( { 3 }^{ 6 } \) ≡ 1 (mod 7)
\( { 3 }^{ 30 } \) ≡ 1 (mod 7)