Question

The number of integral points on the hyperbola x² – y²  = (2000)² is (an integral point is a point both of whose co-ordinates are integer)

(A)  98 

(B)  96 

(C)  48 

(D)  24

Answer 1

Correct option (A) 98 

x² – y²  = 20002 = (24 x 53)²

⇒ (x + y)(x - y) = 2⁸ x 5⁶

For y = 0, x = ± 2000

Let (x > 0, y > 0) x + y and x – y are both even. Then

the number of integral values of x, y = (7 x 7 - 1)/2 = 24

⇒ the number of integral points = 24 x 4 + 2 = 98