Erdős conjecture

Erdős conjecture

The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects.

Some of these are the following:
* The Cameron–Erdős conjecture on sum-free sets of integers, solved by Green.
* The Erdős–Burr conjecture on Ramsey numbers of graphs.
* The Erdős–Faber–Lovász conjecture on coloring unions of cliques.
* The Erdős–Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity.
* The Erdős–Gyárfás conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3.
* The Erdős–Heilbronn conjecture in combinatorial number theory on the number of sums of two sets of residues modulo a prime.
* The Erdős–Mollin–Walsh conjecture on consecutive triples of powerful numbers.
* The Erdős–Menger conjecture on disjoint paths in infinite graphs. ( [http://imu.org.il/neve-ilan/comb.html#combabs apparently solved by Ron Aharoni and Eli Berger] )
* The Erdős–Mordell inequality on distances of pedal points in triangles ( [http://mathworld.wolfram.com/Erdos-MordellTheorem.html MathWorld] )
* The Erdős–Stewart conjecture on the Diophantine equation "n"! + 1 = "p""k""a"" "p""k"+1b" ( [http://www.ams.org/mathscinet-getitem?mr=2001g:11042 solved by Luca] )
* The Erdős–Straus conjecture on the Diophantine equation 4/"n" = 1/"x" + 1/"y" + 1/"z".
* The Erdős conjecture on arithmetic progressions in sequences with divergent sums of reciprocals.
* The Erdős–Woods conjecture on numbers determined by the set of prime divisors of the following "k" numbers.
* The Erdős–Szekeres conjecture on the number of points needed to ensure that a point set contains a large convex polygon.
* A conjecture on quickly growing integer sequences with rational reciprocal series.

External links

* [http://math.ucsd.edu/~fan/ep.pdf Fan Chung, "Open problems of Paul Erdős in graph theory"]


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