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KVPY2017MathematicsSets and Relations

Let S be the set of all ordered pairs (x, y) of positive integers satisfying the condition x²-y²=12345678 . Then

Options

  1. AS is an infinite set
  2. BS is the empty set
  3. CS has exactly one element
  4. DS is a finite set and has at least two elements.

Correct answer

B. S is the empty set

Step-by-step solution

x²-y²=12345678 (x, y I⁺ ) R.H.S. is even, so x , y should be odd integer but difference of square of two odd integers is multiple of 8 but R.H.S. is not multiple of 8

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