If-x-2-y-2-2023-2023-then-how-many-pair-of-x-y-where-x-y-N-

Question Number 191232 by BaliramKumar last updated on 21/Apr/23

If x^{2} - y^{2} = 2023^{2023} then how many

pair of x, y w h e r e x, y \in N

Answered by mr W last updated on 21/Apr/23

2023 = 7 \times 17^{2}

2023^{2023} = 7^{2023} \times 17^{4046}

(x - y) (x + y) = a \times b = 7^{2023} \times 17^{4046}

x - y = a

x + y = b > a

x = \frac{a + b}{2} > y

y = \frac{b - a}{2}

a p a i r o f (a, b) \Rightarrow a p a i r o f (x, y)

n u m b e r o f p a i r s o f (a, b) i s

\frac{(2023 + 1) (4046 + 1)}{2} = 4 095 564

t h a t m e a n s t h e r e a r e 4 095 564 p a i r s

o f x, y .

Commented by BaliramKumar last updated on 21/Apr/23

Thanks Sir