Erdős-Moser Equation

The Diophantine equation

Erdős conjectured that there is no solution to this equation other than the trivial solution , although this remains unproved (Guy 1994, pp. 153-154). Moser (1953) proved that there is no solution for , and Butske et al. (1999) extended this to , or more specifically, .

REFERENCES:

Butske, W.; Jaje, L. M.; and Mayernik, D. R. "The Equation , Pseudoperfect Numbers, and Partially Weighted Graphs." Math. Comput. 69, 407-420, 1999.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, 1994.

Moree, P. "Diophantine Equations of Erdős-Moser Type." Bull. Austral. Math. Soc. 53, 281-292, 1996.

Moser, L. "On the Diophantine Equation ." Scripta Math. 19, 84-88, 1953.