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Question: Answered & Verified by Expert
Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers satisfying the condition $x^{2}-y^{2}=12345678$. Then
MathematicsSets and RelationsKVPYKVPY 2017 (5 Nov SA)
Options:
  • A $S$ is an infinite set
  • B $S$ is the empty set
  • C S has exactly one element
  • D $S$ is a finite set and has at least two elements.
Solution:
1795 Upvotes Verified Answer
The correct answer is: $S$ is the empty set
$x^{2}-y^{2}=12345678\left(x, y \in I^{+}\right)$
R.H.S. is even, so $\mathrm{x}$, 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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