on monochromatic Egyptian fraction representations of unity, proved by Ernie Croot in 2000. The Erdős–Stewart conjecture on the Diophantine equation n! + 1 = pka pk+1b, solved by Florian Luca in 2001. The Cameron–Erdős conjecture on sum-free sets of integers, proved by Ben Green and Alexander Sapozhenko in 2003–2004. The Erdős–Menger conjecture on disjoint paths in infinite graphs, proved by Ron Aharoni and Eli Berger in 2009. The Erdős distinct distances problem. The correct exponent was proved in 2010 by Larry Guth and Nets Katz, but the correct power of log n is still undetermined. The Erdős–Rankin conjecture on prime gaps, proved by Ford, Green, Konyagin, and Tao in 2014. The Erdős discrepancy problem on partial sums of ±1-sequences. Terence Tao announced a solution in September 2015; it was published in 2016. The Erdős squarefree conjecture that central binomial coefficients C(2n, n) are never squarefree for n > 4 was proved in 1996. The Erdős primitive set conjecture that the sum for any primitive set A (a set where no member of the set divides another member) attains its maximum at the set of primes numbers, proved by Jared Duker Lichtman in 2022. The Erdős-Sauer problem about maximum number of edges an n-vertex graph can have without containing a k-regular subgraph, solved by Oliver Janzer and Benny Sudakov See also List of things named after Paul Erdős References External links Fan Chung, "Open problems of Paul Erdős in graph theory" Fan Chung, living version of "Open problems of Paul Erdős in graph theory" Erdos Paul Erdős Conjectures,Erdos