UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Brocard’s Problem

 

Brocard’s Problem concerns the equation

n! + 1 = m²

where n and m are both integers, and n! Is the factorial of n, that is, the product of all integers less than or equal to n (so, for example, 3! = 3*2*1 = 6, and 4! = 4*3*2*1 = 24, etc).

Only three solutions to this equation are known, when n = 4 or 5 or 7.

The problem is to find other values of n for which this equation is true, or to prove that there are no other solutions..

 

For further information, please see:

[1] http://mathworld.wolfram.com/BrocardsProblem.html

[2] http://blogs.ams.org/mathgradblog/2013/08/08/problem-brocard/#sthash.Sl87FtZe.dpbs

[3] http://en.wikipedia.org/wiki/Brocard%27s_problem

 

You can check for contributions to this problem on the solutions page.

 

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Tim S Roberts

Email: timro21@gmail.com

 

Version MC13a .