<s>[INST] Is $(2,5)$ the only solution? Find all pairs $(m,n)\in{\mathbb{N^2}}$ such that 
$$(m^2-1)^3-n^2=2$$
Is  $(2,5)$ the only solution?
 [/INST] Maybe this helps
$(m^2-1)^3-n^2 =2\iff (m^2-1)^3-27=n^2-25$
$\iff (m^2-4)( (m^4-2m^2+1)+3(m^2-1)+9)=(n-5)(n+5)$
$\iff(m+2)(m-2)(m^4+m^2+7)=(n-5)(n+5)$
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