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Let b be an integer greater than 2, and let \(N_b = 1_b + 2_b + \cdots + 100_b \) (the sum contains all valid base b numbers up to \(100_b \)). Compute the number of values of b for which the sum of the squares of the base b digits of \(N_b\) is at most 512.

 Aug 31, 2020
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There are 47 values of b that work.

 Sep 5, 2020

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