Every problem posed by Paul Erdős, with its status, references, discussion and proof claims.
606 of 1,221 problems match
Every problem posed by Paul Erdős, with its status, references, discussion and proof claims.
Asks whether two positive integers x and y must be equal when the primes dividing x to the n minus one match those dividing y to the n minus one for every n.
Asks whether a constant bounds the length of a path from zero to the unit circle inside the region where such a polynomial has modulus below one.
Estimates the largest transitive subtournament every tournament on n vertices must contain; floor(log_2 n) + 1 first fails at n = 14 and fails for infinitely many n; f is known exactly for n <= 33 and 47 <= n <= 56.
Asks whether a sequence of positive lower logarithmic density contains a divisibility chain whose upper growth rate against log log x is at least the weighted sum's; answered yes in 2026 by Alexeev and seven coauthors.
Asks whether a sum of strictly increasing powers two to the aleph n_k, the first above aleph omega, satisfies the partition relation to aleph omega for pairs.
Asks whether a singular cardinal that is aleph-zero-inaccessible, as is its cofinality, satisfies the partition relation to itself and aleph one for pairs.