Solve for integer k,m and n: k^2 m−n^2 =8


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Question Number 216769 by ArshadS last updated on 19/Feb/25

$S o l v e f o r i n t e g e r k, m a n d n :$ $k^{2} m - n^{2} = 8$
	Answered by mehdee7396 last updated on 20/Feb/25

	$‘ ‘ m^{″} m u s t b e p o s i t i v e$ $(\sqrt{m} k + n) (\sqrt{m} k - n) = 8 = 4 \times 2$ $i f k, n > 0 \Rightarrow \sqrt{m} k + n = 4 & \sqrt{k} m - n = 2$ $\Rightarrow n = 1 \Rightarrow \sqrt{m} k = 3$ $1) \sqrt{m} = 1 & k = 3 \Rightarrow m = 1 & k = 3 & n = 1$ $2) \sqrt{m} = 3 & k = 1 \Rightarrow m = 9 & k = 1 & n = 1$ $i f k, n < 0 \Rightarrow< k = - 3 & n = - 1$ $A n s)$ $(m, n, k) : (1, 1, 3), (9, 1, 1), (1, - 1, - 3), (9, - 1, - 3)$
	Commented by ArshadS last updated on 20/Feb/25

	$T h a n k s! S o m e s o l u t i o n s o u t o f m a n y!$ $C a n y o u o r a n y o n e e l s e g e t g e n e r a l s o l u t i o n / s ?$
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