# Discrepancy Conjecture

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In 2015, Terence Tao proved the Erdős discrepancy conjecture [1]. Consider a sequence like , where all the terms are . After that, partition into sections of length , take the first sections, and then total up the last terms in each section. For and , the sections are , , , and ; the final terms are ; and their total is 2. The maximum value obtained by any considered or is the discrepancy.

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Contributed by: Ed Pegg Jr (October 2015)

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References

[1] T. Tao, "The Erdős Discrepancy Problem," 2015. arXiv:1509.05363.

[2] B. Konev and A. Lisitsa, "A SAT Attack on the Erdős Discrepancy Conjecture," in *Theory and Applications of Satisfiability Testing—SAT 2014*, 8561, 2014 pp. 219–226.

[3] B. Konev and A. Lisitsa, "Computer-Aided Proof of Erdős Discrepancy Properties," *Artificial Intelligence*, 224, 2015 pp. 103–118. Data.

[4] "The Erdős Discrepancy Problem." *Polymath*. (Sep 21, 2015) michaelnielsen.org/polymath1/index.php?title=The_Erdős _discrepancy _problem.

[5] Wikipedia. "±1 Sequence." (Sep 30, 2015) en.wikipedia.org/wiki/%C2 % B11-sequence.

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