In number theory, the Erdős–Moser equation is defined as
Of course, a well-known trivial solution is
However, Paul Erdős conjectured that no further solutions exist to the Erdős–Moser equation other than
So, now what?
Well, a solution to find is
Leo Moser also posed certain constraints on the solutions:
. , where is a positive number and that there is no other solution for , which Leo Moser himself proved in .
. , which was shown in .
. divides and that any prime factor of must be irregular and , which was shown in .
. In , Moser's method was extended to show that .
. In , it was shown that must divide , where is all the primes in between.
. In , it was shown that must be a convergent of - large-scale computation was used to show that .