BDMO Primes!

\(p\) is a prime number such that there exist positive integers \(n\) and \(m\) that satisfy the following equation:

\[p^n+144=m^2\]

What is the sum of all possible values of \(m\)?


This problem appeared at the BDMO-2007 regionals.


This problem is from the set "Olympiads and Contests Around the World -1". You can see the rest of the problems here.

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