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

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Albert1

$a,b\in N$

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

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

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Albert1

Albert said:

$a,b\in N$

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

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

$hint:$

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

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