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ABSTRACT: Let p(n) be the partition function. Erdős conjectured that for each integer m, there exists a positive integer n such that p(n) = 0 (mod m). Later, Newman conjectured that for each integer m and r, there are infinitely many positive integers n such that p(n) = r (mod m). In this talk, I will talk about known results on Newman's conjecture on the partition function and our recent progress on the conjecture. This is a joint work with Youngmin Lee.