perplexus.info :: Just Math : Find all possible pairs

Find all possible pairs (Posted on 2023-11-19)

Find all solutions to
(m^2 + n)(m + n^2) = (m - n)^2
where m and n are non-zero integers.

No Solution Yet Submitted by Ady TZIDON

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computer exploration

| Comment 1 of 2

for tot=-99999:99999

for n=-99999:999

m=tot-n;

if (m^2+n)*(m+n^2)==(m-n)^2

disp([m n (m-n)^2])

end

finds only

>> findAllPossiblePairs
    -1    -1     0
     0     0     0
     2    -1     9
     1     0     1
     0     1     1
    -1     2     9

but there may be more beyond the searched bounds.

Excluding the ones that include m or n being zero, what's left are:

m = -1 n = -1    (m-n)^2 = 0
m = 2  n = -1    (m-n)^2 = 9
m = -1 n = 2     (m-n)^2 = 9

Posted by Charlie on 2023-11-19 09:33:18

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