Question

Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers satisfying the condition $x^2-y^2=12345678$. Then

• 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

Answer 1

The correct option is B $S$ is the empty set

$x^2-y^2=(x-y)(x+y)$

and given is $x^2-y^2=12345678$

there is no possible value of $x$ and $y$ such that,

$(x+y)(x-y)=12345678$

so the set of $(x,y)$ will be empty set.