Find all ordered pairs
![(a,b)](/media/m/e/2/6/e263229694cdbeb908488db2d0351f0a.png)
of positive integers for which the numbers
![\dfrac{a^3b-1}{a+1}](/media/m/6/1/7/6176135fd940484d49602888ee243945.png)
and
![\dfrac{b^3a+1}{b-1}](/media/m/f/9/5/f957a55bbbaaa7a8a978fe3176c491b1.png)
are both positive integers.
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Find all ordered pairs $(a,b)$ of positive integers for which the numbers $\dfrac{a^3b-1}{a+1}$ and $\dfrac{b^3a+1}{b-1}$ are both positive integers.