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  • find one factor for 1280000401

    From henhanna@gmail.com@21:1/5 to All on Fri Jul 1 10:56:55 2022
    1. Factorize: 2009

    2. Factorize: ( 81 ^ 3 + 4 )


    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.



    pls wait a few days before posting answers or hints.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Stephen Perry@21:1/5 to henh...@gmail.com on Fri Jul 1 17:06:04 2022
    On Friday, July 1, 2022 at 1:56:56 PM UTC-4, henh...@gmail.com wrote:
    1. Factorize: 2009

    2. Factorize: ( 81 ^ 3 + 4 )


    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.



    pls wait a few days before posting answers or hints.

    interesting, the last one only has 2 prime factors

    swp

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Heathfield@21:1/5 to Stephen Perry on Sat Jul 2 03:06:06 2022
    On 02/07/2022 1:06 am, Stephen Perry wrote:
    On Friday, July 1, 2022 at 1:56:56 PM UTC-4, henh...@gmail.com wrote:
    1. Factorize: 2009

    2. Factorize: ( 81 ^ 3 + 4 )


    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.



    pls wait a few days before posting answers or hints.

    interesting, the last one only has 2 prime factors

    Interesting, one of those two prime factors is strongly related to:

    49670943841842804710155545472491674508546533688809\ 00974054678181809222613988422954258068225897148337\ 95213495222240007671066490851554749892134937936656\ 28299463790905194739834052614993480810633009669295\ 35999447677162583428914287273190484804247505062548\ 45534889774433360425470710774683290442555783815659\ 95587526442752892957567593156343721469275848230250\ 31242105280010233598043558996619044969346638973101\ 50700949162282909151225143677669059060838583122439\ 58597751816029723282726401683087622594082178263812\ 60302214424111544898559326399838404889278853003358\ 33913419474049335611983897922046477193331977853760\ 79498859329368329674820971921713672892086786229753\ 14947040444848309008177329032019450499069829806554\ 81012268737891556187874734833673235166827039350174\ 86350158134726246547741534038937359543777932214369\ 44462684662996874035200000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\
    000000000000000000000000.

    Finding the relationship is left as an exercise ---------- pls
    don't wait as much as a millisecond before posting answers or hints.

    --
    Richard Heathfield
    Email: rjh at cpax dot org dot uk
    "Usenet is a strange place" - dmr 29 July 1999
    Sig line 4 vacant - apply within

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Ilan Mayer@21:1/5 to Richard Heathfield on Sat Jul 2 06:44:58 2022
    On Friday, July 1, 2022 at 10:06:09 PM UTC-4, Richard Heathfield wrote:
    On 02/07/2022 1:06 am, Stephen Perry wrote:
    On Friday, July 1, 2022 at 1:56:56 PM UTC-4, henh...@gmail.com wrote:
    1. Factorize: 2009

    2. Factorize: ( 81 ^ 3 + 4 )


    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.



    pls wait a few days before posting answers or hints.

    interesting, the last one only has 2 prime factors
    Interesting, one of those two prime factors is strongly related to:

    49670943841842804710155545472491674508546533688809\ 00974054678181809222613988422954258068225897148337\ 95213495222240007671066490851554749892134937936656\ 28299463790905194739834052614993480810633009669295\ 35999447677162583428914287273190484804247505062548\ 45534889774433360425470710774683290442555783815659\ 95587526442752892957567593156343721469275848230250\ 31242105280010233598043558996619044969346638973101\ 50700949162282909151225143677669059060838583122439\ 58597751816029723282726401683087622594082178263812\ 60302214424111544898559326399838404889278853003358\ 33913419474049335611983897922046477193331977853760\ 79498859329368329674820971921713672892086786229753\ 14947040444848309008177329032019450499069829806554\ 81012268737891556187874734833673235166827039350174\ 86350158134726246547741534038937359543777932214369\ 44462684662996874035200000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\
    000000000000000000000000.

    Finding the relationship is left as an exercise ---------- pls
    don't wait as much as a millisecond before posting answers or hints.

    --
    Richard Heathfield
    Email: rjh at cpax dot org dot uk
    "Usenet is a strange place" - dmr 29 July 1999
    Sig line 4 vacant - apply within

    421 is a factor of 1280000401; the above number is 421! (factorial of 421).

    Please reply to ilanlmayer at gmail dot com

    __/\__
    \ /
    __/\\ //\__ Ilan Mayer
    \ /
    /__ __\ Toronto, Canada
    /__ __\
    ||

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From henhanna@gmail.com@21:1/5 to Ilan Mayer on Sat Jul 2 07:21:39 2022
    On Saturday, July 2, 2022 at 6:45:00 AM UTC-7, Ilan Mayer wrote:
    On Friday, July 1, 2022 at 10:06:09 PM UTC-4, Richard Heathfield wrote:
    On 02/07/2022 1:06 am, Stephen Perry wrote:
    On Friday, July 1, 2022 at 1:56:56 PM UTC-4, henh...@gmail.com wrote:
    1. Factorize: 2009

    2. Factorize: ( 81 ^ 3 + 4 )


    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.



    pls wait a few days before posting answers or hints.

    interesting, the last one only has 2 prime factors
    Interesting, one of those two prime factors is strongly related to:

    49670943841842804710155545472491674508546533688809\ 00974054678181809222613988422954258068225897148337\ 95213495222240007671066490851554749892134937936656\ 28299463790905194739834052614993480810633009669295\ 35999447677162583428914287273190484804247505062548\ 45534889774433360425470710774683290442555783815659\ 95587526442752892957567593156343721469275848230250\ 31242105280010233598043558996619044969346638973101\ 50700949162282909151225143677669059060838583122439\ 58597751816029723282726401683087622594082178263812\ 60302214424111544898559326399838404889278853003358\ 33913419474049335611983897922046477193331977853760\ 79498859329368329674820971921713672892086786229753\ 14947040444848309008177329032019450499069829806554\ 81012268737891556187874734833673235166827039350174\ 86350158134726246547741534038937359543777932214369\ 44462684662996874035200000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 000000000000000000000000.

    Finding the relationship is left as an exercise ---------- pls
    don't wait as much as a millisecond before posting answers or hints.

    --
    Richard Heathfield
    Email: rjh at cpax dot org dot uk
    "Usenet is a strange place" - dmr 29 July 1999
    Sig line 4 vacant - apply within
    421 is a factor of 1280000401; the above number is 421! (factorial of 421).




    i should have emphasized... that ....
    all these problems are...

    What formula do you use (as shortcuts) in doing these factorizations by hand (or in your head) ?

    1. Factorize: 2009 ----------- ans: the formula for (x^2 - y^2) = ...............


    2. Factorize: ( 81 ^ 3 + 4 ) .........

    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Heathfield@21:1/5 to Ilan Mayer on Sat Jul 2 16:42:44 2022
    On 02/07/2022 2:44 pm, Ilan Mayer wrote:
    On Friday, July 1, 2022 at 10:06:09 PM UTC-4, Richard Heathfield wrote:
    On 02/07/2022 1:06 am, Stephen Perry wrote:
    On Friday, July 1, 2022 at 1:56:56 PM UTC-4, henh...@gmail.com wrote:
    1. Factorize: 2009

    2. Factorize: ( 81 ^ 3 + 4 )


    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.



    pls wait a few days before posting answers or hints.

    interesting, the last one only has 2 prime factors
    Interesting, one of those two prime factors is strongly related to:

    49670943841842804710155545472491674508546533688809\
    00974054678181809222613988422954258068225897148337\
    95213495222240007671066490851554749892134937936656\
    28299463790905194739834052614993480810633009669295\
    35999447677162583428914287273190484804247505062548\
    45534889774433360425470710774683290442555783815659\
    95587526442752892957567593156343721469275848230250\
    31242105280010233598043558996619044969346638973101\
    50700949162282909151225143677669059060838583122439\
    58597751816029723282726401683087622594082178263812\
    60302214424111544898559326399838404889278853003358\
    33913419474049335611983897922046477193331977853760\
    79498859329368329674820971921713672892086786229753\
    14947040444848309008177329032019450499069829806554\
    81012268737891556187874734833673235166827039350174\
    86350158134726246547741534038937359543777932214369\
    44462684662996874035200000000000000000000000000000\
    00000000000000000000000000000000000000000000000000\
    000000000000000000000000.

    Finding the relationship is left as an exercise ---------- pls
    don't wait as much as a millisecond before posting answers or hints.

    421 is a factor of 1280000401; the above number is 421! (factorial of 421).

    All those 0s at the end are a dead giveaway, aren't they?

    --
    Richard Heathfield
    Email: rjh at cpax dot org dot uk
    "Usenet is a strange place" - dmr 29 July 1999
    Sig line 4 vacant - apply within

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Tobin@21:1/5 to rjh@cpax.org.uk on Sat Jul 2 16:04:05 2022
    In article <t9pp1k$2l9tj$1@dont-email.me>,
    Richard Heathfield <rjh@cpax.org.uk> wrote:


    ...
    44462684662996874035200000000000000000000000000000\
    00000000000000000000000000000000000000000000000000\
    000000000000000000000000.

    421 is a factor of 1280000401; the above number is 421! (factorial of 421).

    All those 0s at the end are a dead giveaway, aren't they?

    And - assuming it is a factorial - the number of 0s (103) quickly
    tells you it's between 420 and 424 factorial.

    -- Richard

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Pancho@21:1/5 to henh...@gmail.com on Sun Jul 3 16:37:29 2022
    On 01/07/2022 18:56, henh...@gmail.com wrote:
    1. Factorize: 2009

    2. Factorize: ( 81 ^ 3 + 4 )


    3. find one factor for 1280000401 ---------- pls wait a few days before posting answers or hints.



    pls wait a few days before posting answers or hints.


    1. Is Fermat factorization 45^2-4^2 = (45+4)(45-4) = 49*41

    2. Is Fermat's little theorem

    3. Dunno

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Pancho@21:1/5 to Pancho on Sun Jul 3 18:21:31 2022
    On 03/07/2022 16:37, Pancho wrote:


    2. Is Fermat's little theorem

    Sorry ignore that. I don't know what I was thinking :-(

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)