THEOREM OF THE DAY: The Erdos Discrepancy Problem

Theorem

Let C be a positive integer and let $( xi)_{i ≥1}$ be an infinite sequence of values from {−1, 1}. Then there exist positive integers d, n, for which the sum $x_d + x_{2d} + . . . + x_{(n −1)d} + x_{nd}$ exceeds C in absolute value.

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