An Easy IMO Problem!

Number Theory Level 3

dd is a positive integer not equal to 2,52, 5 or 1313. How many values of dd are there such that for any pair (a,b)(a, b) from the set {2,5,13,d}\{2, 5, 13, d\}, ab−1ab-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.
Mursalin Habib by Mursalin Habib
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