Authors: Arkoprobho Chakraborty
Comments: 13 pages.
Erdos had conjectured that the equation of the title had no solutions
in natural numbers except the trivial 11 + 21 = 31. Moser (1953) had
shown that there are no solutions for M+1 < 10106. Butske et al (1993)
had further shown that there are no solutions for M+1 < 9.3x106. In
this paper I show that a solution to this equation cannot exist for any
value of M > 2 hence proving Erdos' conjecture. This is achieved using
elementary number theoretic methods employing congruences and well-known identities.
Category: Number Theory