MHB Find Integer Solutions to $k=\dfrac{ab^2-1}{a^2b+1}$

[Albert1]

$a,b\in N$

$k=\dfrac {ab^2-1}{a^2b+1}\,\, \,also \,\,\in N$

find pair(s) of $(a,b)$

 

[Albert1]

$a,b\in N$

$k=\dfrac {ab^2-1}{a^2b+1}\,\, \,also \,\,\in N$

find pair(s) of $(a,b)$

$hint:$

Spoiler

$if \,\,a=1\,\, then \,\,b=?$
$if \,\,a>1\,\, then \,\,no \,\,solution.\,\, why ?$