arXiv:1602.06208math.NT
Every positive integer is a sum of three palindromes
Abstract
For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
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Linked by 4 identifiable commenters in 5 comments across 2 threads, from Sep 2018 to Sep 2024. Found in 1 HN submission from Mar 2018 to Mar 2018. Open submission discussions.
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You may find the original paper proving this more impressive: https://arxiv.org/abs/1602.06208
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For those wondering, this works in every base ≥ 5, according to the original paper: https://arxiv.org/abs/1602.06208v2 Every time I see something like this that is dependent on base-10 representation, I'm always curious to know whether it generalizes, or if it's a quirk specific…
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Not base 2. All palindromes in base 2 have a 1 in the last position, because there's a 1 in the first position. This means that any addition of 3 palindromes must be odd because the result of the addition is guaranteed a 1 in the ones position, meaning even numbers can't…
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Well, there is a whole 40+ page paper on the algorithm and its proof of correctness. So, yes there is an answer. https://arxiv.org/abs/1602.06208
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Quite miraculous. Underlying paper: https://arxiv.org/abs/1602.06208v2 Unfortunately, the algorithm seems to be a bit too complex to turn this into a party trick.
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