What is the remainder when \( { 3 }^{ 19 - CUETMOCK

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Other - Maths Section B1

Question:

What is the remainder when \( { 3 }^{ 19 } \) is divided by 7?

Options:

3

4

5

6

Correct Answer:

3

Explanation:

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)

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