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fermatslibrary's profile
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 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary 14 Nov 2019
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    Liouville proved the following property of the divisors of the divisors of a number: 1) Start with a number (e.g. 10) 2) Write down its divisors (1,2,5,10) 3) Write down the number of divisors of each divisor (1,2,2,4) 4) (1+2+2+4)²=81=1³+2³+2³+4³pic.twitter.com/ZqiL5pu5I2

    6:30 AM - 14 Nov 2019
    • 896 Retweets
    • 4,419 Likes
    • Cristian Viramontes Cəfər Andrew Lytle AieKick Mvs Sanjay Thamsanqa Dimitrios Kalemis Yousaf Hussain Alisa💞
    43 replies 896 retweets 4,419 likes
      1. DℝOℕ∈‏ @d_r_o_n_e 14 Nov 2019
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        Replying to @fermatslibrary

        Liouville’s tau generalizationpic.twitter.com/uZU3SJcqMZ

        0 replies 13 retweets 106 likes
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      2. K E L L S  🧑🏻‍🚀‏ @Kelly_StOnge 14 Nov 2019
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        Replying to @fermatslibrary

        Had to try it with a prime. Still works.

        1 reply 0 retweets 15 likes
      3. Franck Lebeau‏ @_Kcnarf 14 Nov 2019
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        Replying to @Kelly_StOnge @fermatslibrary

        And final result is always the same: 9. 1) start with a prime => P 2) divisors => always [1, P] 3) number of divisors of each divisor => always [1,2] (1 divisible by 1, P divisible by 1 and P) 4) (1+2)²=1³+2³=9, always 😀

        1 reply 3 retweets 55 likes
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      2. Fernando Arizmendi‏ @ferariz 14 Nov 2019
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        Replying to @fermatslibrary

        Nice! That reminds me a similar relation that I found when I was at high school: (1+2+3+...+N)^2 = (1^3+2^3+3^3+...+N^3)

        4 replies 4 retweets 18 likes
      3. Σ(i³) = (Σi)²‏ @SvenGeier 14 Nov 2019
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        Replying to @ferariz @fermatslibrary

        You called?

        0 replies 0 retweets 16 likes
      4. End of conversation
      1. New conversation
      2. Roger Sauer‏ @rsauer3473 14 Nov 2019
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        Replying to @fermatslibrary

        How about this one since I don’t do math well? Number of English/Arabic numerals composed of only straight lines (1,4,7)= 3, a prime Number of English/Arabic numerals composed with curved lines (2,3,5,6,8,9,0)= 7, a prime Does the Fields Medal come with any cash?

        2 replies 0 retweets 23 likes
      3. Zack Higgins‏ @GitCommitIssues 14 Nov 2019
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        Replying to @rsauer3473 @fermatslibrary

        To be frank, I believe curved numbers are just a quirk of how we write Arabic numerals for modern convenience; that is, the original symbols were straight and their values were based on the number of angles in the symbol.

        1 reply 0 retweets 12 likes
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      2. Itohan‏ @EmmanuelSalau 14 Nov 2019
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        Replying to @fermatslibrary

        Any application?

        1 reply 0 retweets 3 likes
      3. Ujjwal Rajput‏ @ujjwalrajput_ 14 Nov 2019
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        Replying to @EmmanuelSalau @fermatslibrary

        Fun

        1 reply 1 retweet 87 likes
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      2. Guillaume Hugot‏ @GuillaumeHgt 14 Nov 2019
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        Replying to @fermatslibrary

        8 (1, 2, 4, 8) (1, 2, 3, 4) (1+2+3+4)^2 = 1^3+2^3+3^3+4^3 = 100 OK

        1 reply 0 retweets 3 likes
      3. Guillaume Hugot‏ @GuillaumeHgt 14 Nov 2019
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        Replying to @GuillaumeHgt @fermatslibrary

        let's try with 2820 :

        1 reply 0 retweets 3 likes
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