The Erdős–Turán Conjecture is a hypothesis in combinatorial number theory proposed by mathematicians Paul Erdős and Pál Turán in 1936. It suggests that for any positive integer k , there exists a constant c_k such that any set of integers with positive density contains a subset of k elements whose sum is divisible by k . This conjecture highlights the relationship between number theory and combinatorics, emphasizing how structured patterns can emerge from seemingly random sets of numbers. Despite extensive research, the conjecture remains unproven for most values of k .