Let
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
be any positive integer not equal to
![2, 5](/media/m/d/c/2/dc2b6641d3bff789b91c64ff2ac7b387.png)
or
![13](/media/m/a/f/0/af007727d79ff468853d32d8393cc8de.png)
. Show that one can find distinct
![a,b](/media/m/7/d/8/7d8bdace47e602448e6040957d8cf923.png)
in the set
![\{2,5,13,d\}](/media/m/c/4/0/c40587832c941716e285b54bb3f70185.png)
such that
![ab-1](/media/m/9/8/9/98911fe6256838b490a47ca451a2aa1f.png)
is not a perfect square.
%V0
Let $d$ be any positive integer not equal to $2, 5$ or $13$. Show that one can find distinct $a,b$ in the set $\{2,5,13,d\}$ such that $ab-1$ is not a perfect square.