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Nov 23, 2021 at 2:24 history edited Noam D. Elkies CC BY-SA 4.0
fix mistake in indexing the sum for $F$, and also correct two minor typos (missing ")", and \cdots for \ldots)
Nov 20, 2021 at 22:16 comment added T. Amdeberhan I like it. Thank you.
Nov 20, 2021 at 22:09 comment added Noam D. Elkies More or less the same, yes (and it would be closer if I organized the argument so that it never explicitly uses $(a+b)^{2^r} \equiv a^{2^r} + b^{2^r}$ for $r > 1$); but I think that formulating it in terms of generating functions shows more clearly what's going on.
Nov 20, 2021 at 22:04 comment added Sam Hopkins I think this is basically the same as the proof by Koshy and Salmassi linked to in Carlo Beenakker's answer.
Nov 20, 2021 at 22:02 history answered Noam D. Elkies CC BY-SA 4.0