An Easy IMO Problem!

\(d\) is a positive integer not equal to \(2, 5\) or \(13\). How many values of \(d\) are there such that for any pair \((a, b)\) from the set \(\{2, 5, 13, d\}\), \(ab-1\) is a perfect square?

This is IMO 1986 -1.
This problem is a part of the set "Olympiads and Contests Around the World - 2". You can see rest of the problems here.
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