Question

What is the remainder when 27²⁷ - 15²⁷ is divided by 6?

Answer 1

Correct Answer - Option 1 : 0

Given:

The given expression 27²⁷ - 15²⁷ 

Calculation                            

N = 27²⁷ - 15²⁷ 

27²⁷ = (21 + 6)²⁷ = 27c₀ (21)²⁷ + 27c₁ (21)²⁷ (6)¹ +  -  -  - -  -   + 27c₂₇(21)⁰  (6)²⁷

15²⁷ = (21 – 6)²⁷ = 27c₀ (21)²⁷ - 27c₁ (21)²⁷ (6)¹ -  -  -  - -  -   - 27c₂₇(21)⁰  (6)²⁷

N = 27²⁷ - 15²⁷ is divided by 6

Here, 6^N/ 6 and obtain remainder = 0

Hence, the 27²⁷ - 15²⁷ is remainder = 0