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Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

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Joined September 2015

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    Fermat's Library‏ @fermatslibrary 18 Apr 2018
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    Here's a curious fact: decimal palindromic numbers with an even number of digits are divisible by 11pic.twitter.com/Z4o7i0ObwJ

    5:50 AM - 18 Apr 2018
    • 639 Retweets
    • 2,457 Likes
    • Powehi NAGENDRA Y إسلام El Artista Anteriormente Conocido Como Jose Chavez Mauro Filippini a bell pepper AGGS_puzzleclub Kāryadweѕнι 🇮🇳
    29 replies 639 retweets 2,457 likes
      1. New conversation
      2. Kartik कार्तिक‏ @ghost__particle 18 Apr 2018
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        Replying to @fermatslibrary

        Why do we always have people questioning the base of the numbers or asking for proofs?

        1 reply 0 retweets 2 likes
      3. 𝖕 | #MassTestingNowPH  ⚔️ 🛡️‏ @xdoublestar 18 Apr 2018
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        Replying to @ghost__particle @fermatslibrary

        As a wise man once said: if it works only in base 10, it's numerology, not number theory.

        1 reply 4 retweets 42 likes
      4. 1 more reply
      1. New conversation
      2. Peter R. Rizun‏ @PeterRizun 18 Apr 2018
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        Replying to @fermatslibrary

        That is so weird. I had to confirm it by trying lots of combinations in Mathematica to believe it was true.

        3 replies 0 retweets 1 like
      3. Jacob Eliosoff‏ @JaEsf 18 Apr 2018
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        Replying to @PeterRizun @fermatslibrary

        Makes sense b/c every (eg) 6-digit palindrome can be made by adding & subtracting multiples of 001100, 011110, 111111, all divisible by 11

        3 replies 1 retweet 14 likes
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      2. Max DeMorgan‏ @MCDeMorgan 19 Apr 2018
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        Replying to @fermatslibrary

        I discovered you can do this when I was 14. But basically any number times 11 works. I recently discovered the same method works for every number. Eg 16.5 is 11 x 1.5, use the method above eg 16.5 x 52 gets 572 then times by 1.5 and boom 858. Eg 33 times 56 gets 616 times 3 =1848pic.twitter.com/KKn5mPh8wF

        1 reply 1 retweet 3 likes
      3. Max DeMorgan‏ @MCDeMorgan 19 Apr 2018
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        Replying to @MCDeMorgan @fermatslibrary

        Using the same method you can make an alternative version of Pascal’s trianglepic.twitter.com/U28ZXxCnmS

        2 replies 0 retweets 3 likes
      4. 4 more replies
      1. George W. Harris‏ @BullCityFats 18 Apr 2018
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        Replying to @fermatslibrary

        True for any base, follows from (n^2i +1) = (n+1) * (n^(2i-1)-n^(2i-2)+...-n+1) (since any even-digit palindromic number is a sum of multiples of (n^2i+1) for various i)

        0 replies 0 retweets 8 likes
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      1. New conversation
      2. カルム  🎗 Calem Smith  🏳️‍🌈 🇭🇰 🇮🇷 🇮🇳 | ミカ‏ @CalemJohnSmith 19 Apr 2018
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        Replying to @fermatslibrary @mindstatex

        Oooo pretty....pic.twitter.com/Ui6XEqdWFA

        1 reply 0 retweets 2 likes
      3. $Reina Nakamoto  🕊‏ @mindstatex 19 Apr 2018
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        Replying to @CalemJohnSmith @fermatslibrary

        11, one of the coolest numbers besides 42.

        0 replies 0 retweets 3 likes
      4. End of conversation
      1. Jacob Rose  🗽‏ @jickup 18 Apr 2018
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        Replying to @fermatslibrary

        People old enough to need to do math in their heads know this the other way around, as the shortcut for multiplying by 11. I haven’t seen it this way around before, but I like it!

        0 replies 0 retweets 3 likes
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