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A conjecture on equitable colorings proven in 1970 by András Hajnal and Endre Szemerédi and now known as the Hajnal–Szemerédi theorem.[1] The Erdős–Lovász conjecture on weak/strong delta-systems, proved by Michel Deza in 1974.[2] The Erdős–Heilbronn conjecture in combinatorial number theory on the number of sums of two sets of residues modulo a prime, proved by Dias da Silva and Hamidoune in 1994.[3] The Erdős–Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity, proved by Ernie Croot in 2000.[4] The Erdős–Stewart conjecture on the Diophantine equation n! + 1 = pka pk+1b, solved by Luca in 2001.[5] The Cameron–Erdős conjecture on sum-free sets of integers, proved by Ben Green and Alexander Sapozhenko in 2003–2004.[6] The Erdős–Menger conjecture on disjoint paths in infinite graphs, proved by Ron Aharoni and Eli Berger in 2009.[7] The Erdős distinct distances problem, solved in 2010 by Larry Guth and Nets Katz.[8] |
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