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Fermat's Library
Fermat's Library
Fermat's Library
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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 Mar 27
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    • Report NetzDG Violation

    Narcissistic Numbers An n-digit number that is the sum of the n-th powers of its digits is called an n-narcissistic. For n=3 there are only 4 numbers - 153, 370, 371, 407 - which are the sums of the cubes of their digits.pic.twitter.com/8iOqXRdEvP

    6:37 AM - 27 Mar 2020
    • 1,111 Retweets
    • 4,310 Likes
    • Matthew Hilton (Matty Hills) 𝘿𝙞𝙠𝙤(◔‿◔) Ashish Ongari blueBird Khetha Dlamini abrajolas Rahul Bhimani simple_sain GregorioFernandez
    36 replies 1,111 retweets 4,310 likes
      1. Maths Ed‏ @MathsEdIdeas Mar 28
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        Replying to @fermatslibrary

        There are 88 narcissistic numbers, from 153 (1³ + 5³ + 3³) to 115,132,219,018,763,992,565,095,597,973,971,522,401 (1³⁹ + 1³⁹ + 5³⁹ + 1³⁹ + 3³⁹ + 2³⁹ + ... + 2³⁹ + 2³⁹ + 4³⁹ + 0³⁹ + 1³⁹), but other than 1, there is only 1 Münchhausen number http://bit.ly/2LZkIk5 :pic.twitter.com/A81MbEANMX

        0 replies 12 retweets 56 likes
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      2. ニルス‏ @Nirusu_99 Mar 27
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        Replying to @fermatslibrary

        Sexy primes are still my favorite https://en.m.wikipedia.org/wiki/Sexy_prime 

        2 replies 1 retweet 23 likes
      3. Nabila fatema‏ @Nabilafatema2 Mar 27
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        Replying to @Nirusu_99 @fermatslibrary

        Sexy prime 😄😆pic.twitter.com/19z68VrK0j

        0 replies 0 retweets 5 likes
      4. End of conversation
      1. New conversation
      2. SriCharan‏ @SriCharan79 Mar 27
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        Replying to @fermatslibrary

        Aren't they called Armstrong numbers?

        1 reply 0 retweets 16 likes
      3. halikarnasfish‏ @Halikarnasfish Mar 27
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        Replying to @SriCharan79 @fermatslibrary

        Yes, you can call it in that way. Same thing.

        0 replies 0 retweets 13 likes
      4. End of conversation
      1. New conversation
      2. Euclid Point‏ @euclidpoint Mar 27
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        Replying to @fermatslibrary

        All 1-digit numbers are trivially narcissistic. In base 10, if an n-digit number is narcissistic, n ∈ {1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 17, 19, 20, 21, 23, 24, 25, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39}. The largest one is 115132219018763992565095597973971522401.

        3 replies 2 retweets 30 likes
      3. Nikhil Bhondekar‏ @NikhilBhondekar Mar 27
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        Replying to @euclidpoint @fermatslibrary

        If all the one digit numbers are narcissistic, then why is 2 not included in here?

        2 replies 0 retweets 2 likes
      4. 2 more replies
      1. New conversation
      2. Roger Sauer‏ @rsauer3473 Mar 27
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        Replying to @fermatslibrary

        Amazingly these were the same numbers chosen by Mrs. Edna Twattenham in the raffle at St. George’s church in Sprawling. Her winnings of £327 were used to reupholster her husband Carl with a lovely chintz fabric with floral highlights.

        1 reply 0 retweets 15 likes
      3. abunajma‏ @peb252 Mar 27
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        Replying to @rsauer3473 @fermatslibrary

        English please

        0 replies 0 retweets 3 likes
      4. End of conversation
      1. New conversation
      2. Alkeif‏ @Alkeif2 Mar 27
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        Replying to @fermatslibrary

        Are there 2-digit examples of this?

        2 replies 0 retweets 1 like
      3. Andreas‏ @spenglerandreas Mar 27
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        Replying to @Alkeif2 @fermatslibrary

        Since 10a_2 + a_1 = a_2^2 + a_1^2 is equivalent to a_2(10- a_2) = a_1(a_1 - 1) and this equation has no solution for a_1,a_2 in {0,...,9}, the answer is no.

        2 replies 0 retweets 4 likes
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