x-2-y-2-2023-x-y-N-How-many-pair-of-x-y-

Question Number 188753 by BaliramKumar last updated on 19/Mar/23

x^{2} - y^{2} = 2023 x, y \in N

H o w m a n y p a i r o f (x, y)

Answered by BaliramKumar last updated on 19/Mar/23

s o l u t i o n : -

x^{2} - y^{2} = 2023

d = 2023

d = 2023 = 7^{1} \times 17^{2}

t o t a l f a c t o r o f 2023 = (1 + 1) (2 + 1) = 6

N o . o f p a i r s (x, y) = ⌊ \frac{6}{2} ⌋ = 3

\begin{matrix} 2023 = 1 \times 2023 \\ 2023 = 7 \times 289 \\ 2023 = 17 \times 119 \end{matrix}} 3 p a i r {\begin{cases} (1012, 1011) \\ (148, 141) \\ (68, 51) \end{cases}

x = \frac{2023 + 1}{2} = 1012, y = \frac{2023 - 1}{2} = 1011

x = \frac{289 + 7}{2} = 148, y = \frac{289 - 7}{2} = 141

x = \frac{119 + 17}{2} = 68, y = \frac{119 - 17}{2} = 51

P a i r = ⌊ ∣ \frac{N o . o f e v e n f a c t o r - N o . o f o d d f a c t o r}{2} ∣ ⌋