The Erdős-Mahler conjecture asserts that an irrational number is a Liouville number if infinitely
many of its regular continued fraction convergents 
have 
bounded by a fixed constant, where 
is the largest prime factor
of 
for a nonzero integer 
, with 
(Erdős and Mahler 1939, Marques 2026). The
condition restricts the prime factors of both the
numerator and the denominator
along the same infinite subsequence.
Marques (2026) reports that, for every finite real number 
, there is a Cantor
set 
such that every 
has irrationality measure 
and infinitely many regular continued
fraction convergents of the form 
, with 
and 
positive integers. The
claimed construction would refute the conjecture, since finite irrationality
measure excludes Liouville numbers.
