NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The remainder when 2 2003 is divided by 17 is

Options

Correct answer

C. 8

Step-by-step solution

2 2003 = 2 3 2 2000 = 8 2 4 500 = 8 16 500 = 8 17 - 1 500 = 8 C 500 0 ⋅ 17 500 - C 500 1 ⋅ 17 499 + . … … . . - C 500 499 ⋅ 17 + C 500 500 = 8 17 k + 1 = 8 × 17 k + 8 So, the remainder obtained is 8 .

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