Mathe­matics may be all about solving problems, but there are certain unsolved problems, problems for which no efficient algorithm exists. Strangely, this is actually a good thing, because the field of cryptog­raphy, which forms a basis for computer security, makes use of such problems to create secure algorithms that cannot be broken easily.

One such problem is the discrete logarithm problem -

Given:
p, a very large prime
a (mod p)
a^x (mod p)

Find: x

This problem is believed to be a ‘hard’ problem, but not proved to be a ‘hard’ problem. Appar­ently, mathe­mati­cians are having a hard time with the proof!

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