Waring’s Theorem for Binary Powers

Combinatorica, pp. 1335-1350, 2019.

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11B13 68R15

Abstract:

A natural number is a binary k’ th power if its binary representation consists of k consecutive identical blocks. We prove, using tools from combinatorics, linear algebra, and number theory, an analogue of Waring’s theorem for sums of binary k’th powers. More precisely, we show that for each integer k> 2, there exists an effectively compu...More

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