Number of integral solution of Diophantine equation

Number Theory Level 2

Let $Z$ be the set of positive integers and $x,y$ belong to $Z$ .Number of all ordered pair ( $x,y$ ) such that $x$ and $y$ satisfied the equation $x$ $^2$ - $y$ $^2$ =666 is _ _ _ _ .

1 None of the above 0 5

1 solution

Taisanul Haque
Oct 29, 2018

Since square of any positive integer is congruent to $0,1$ ( $mod 4$ ) i.e $x$ $^2$ $\equiv$ $0,1$ ( $mod 4$ ) similarly for $y$ $^2$ .

Now $x$ $^2$ - $y$ $^2$ $\equiv$ $0,1,3$ ( $mod 4$ ) but $666$ $\equiv$ $2$ ( $mod 4$ ). hence this equation has $0$ solution

Number of integral solution of Diophantine equation

1 solution

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