In 1930s Paul Erdos conjectured that for any positive integer C in any infinite ±1 sequence (x_n) there exists a subsequence x_d, x_(2d), x_(3d),...,x_(kd), for some positive integers k and d, such that |∑_(i=1)~k x_(id)| > C. The conjecture has been referred to as one of the major open problems in combinatorial number theory and discrepancy theory. For the particular case of C = 1 a human proof of the conjecture exists; for C = 2 a bespoke computer program had generated sequences of length 1124 of discrepancy 2, but the status of the conjecture remained open even for such a small bound. We show that by encoding the problem into Boolean satisfiability and applying the state of the art SAT solver, one can obtain a discrepancy 2 sequence of length 1160 and a proof of the Erdos discrepancy conjecture for C = 2, claiming that no discrepancy 2 sequence of length 1161, or more, exists. We also present our partial results for the case of C = 3.
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