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KCET2010MathematicsMathematical Reasoning

The least positive integer x satisfying 2²⁰¹⁰ 3 x( 5) is

Options

  1. A3
  2. B4
  3. C1
  4. D2

Correct answer

A. 3

Step-by-step solution

Since, we know that 2² -1( 5) ( 2²+1 . divisible by 5 ) Now, 2²⁰¹⁰= (2² )¹⁰⁰⁵ (-1)¹⁰⁰⁵( 5) 2²⁰¹⁰ -1( 5) -1 2²⁰¹⁰( 5) But 2²⁰¹⁰ 3 x( 5) -1 3 x( 5) (by transitive relation) x=3

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