2026-05-26 02:15 UTC
Replies (2)
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@drScott@mathstodon.xyz 2026-05-26 05:08
@benleis@mathstodon.xyz We should probably rewrite that as $3^15 + 3 \cdot 3^10 + 3 \cdot 3^5 + 1$, and perhaps look at a triangle.
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@gjm@mathstodon.xyz 2026-05-26 09:19
@benleis@mathstodon.xyz I solved it (took maybe 10 minutes or so?) and thought "yay, today I'm being smarter than Some Guy On The Internet". Then started writing up a solution in case anyone cared. Then thought "I bet there's a nice slick way to do it once you already know the answer". Then thought: D'oh! (Sketch of the ugly solution, which would actually be a little bit clever if there weren't something so much easier available: at first glance this looks like you're going to multiply by something like 3^5+3^4+...+1 and get an easily-summed g.p.; this doesn't quite work because the exponents aren't equally spaced; but if you multiply by 3^4+...+1 then you get that easily summed g.p. plus a couple of correction terms, and then the whole thing falls apart into factors of 3^5 +- 1.) I am not sure whether @drScott@mathstodon.xyz has in fact solved the whole thing the neat way and is just being coy about it, or whether he is going to have an even bigger d'oh! moment than I did.