Comments on: My Vision for Number Gossip
https://blog.tanyakhovanova.com/2022/05/my-vision-for-number-gossip/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Thu, 05 May 2022 17:31:16 +0000
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By: Shreevatsa
https://blog.tanyakhovanova.com/2022/05/my-vision-for-number-gossip/#comment-13439
Thu, 05 May 2022 17:31:16 +0000https://blog.tanyakhovanova.com/?p=1627#comment-13439About the last line (26 is the only integer between two non-trivial powers), note that it is the n=2 case of a conjecture that for n=1 is called Catalan’s conjecture (that 8 and 9 are the only two nontrivial powers with a difference of 1) and was proved in 2002: https://en.wikipedia.org/wiki/Catalan%27s_conjecture — I don’t know whether the n=2 case has been proved or is still open, but it may be hard.
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By: Jon Awbrey
https://blog.tanyakhovanova.com/2022/05/my-vision-for-number-gossip/#comment-13438
Sun, 01 May 2022 15:25:50 +0000https://blog.tanyakhovanova.com/?p=1627#comment-13438Here’s a bit of info about an interesting number I encountered recently —

I noticed it had a property I dubbed “Squarefree All The Way Down” (SATWD).

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By: Jon Awbrey
https://blog.tanyakhovanova.com/2022/05/my-vision-for-number-gossip/#comment-13437
Sun, 01 May 2022 15:00:21 +0000https://blog.tanyakhovanova.com/?p=1627#comment-13437Here’s a resource for exploring many novel properties of numbers —