CUET Preparation Today
| What is the remainder when \( { 4 }^{ 40 } \) is divided by 7? |
1 2 3 4 |
| 4 |
| By Fermat's theorem \( { 4 }^{ 7-1 } \) ≡ 1 (mod 7) \( { 4 }^{ 6 } \) ≡ 1 (mod 7) \( { 4 }^{ 36 } \) ≡ 1 (mod 7) \( { 4 }^{ 40 } \) ≡ 256 (mod 7) ≡ 4 (mod 7) |
