Solve-for-integer-k-m-and-n-k-2-m-n-2-8-

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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