The Erdős–Stewart conjecture on the Diophantine equation n! + 1 = p_k^a pk+1^b (solved by Luca)

A conjecture on quickly growing integer sequences with rational reciprocal series.

The Erdős–Mollin–Walsh conjecture on consecutive triples of powerful numbers.

The Erdős–Szekeres conjecture on the number of points needed to ensure that a point set contains a large convex polygon.

The Erdős–Straus conjecture on the Diophantine equation 4/n = 1/x + 1/y + 1/z.

The Erdős–Faber–Lovász conjecture on coloring unions of cliques.

The Erdős–Heilbronn conjecture in combinatorial number theory on the number of sums of two sets of residues modulo a prime.

The Erdős–Graham conjecture in combinatorial number theory on monochromatic Egyptian fraction representations of unity.

The Erdős–Burr conjecture on Ramsey numbers of graphs.

The Erdős–Woods conjecture on numbers determined by the set of prime divisors of the following k numbers.

The Erdős–Gyárfás conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3.

The Erdős conjecture on arithmetic progressions in sequences with divergent sums of reciprocals.

The Erdős–Mordell inequality on distances of pedal points in triangles (MathWorld)

The Cameron–Erdős conjecture on sum-free sets of integers, solved by Green.

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: