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Posers and Puzzles

Posers and Puzzles

  1. Standard member genius
    Wayward Soul
    01 Mar '05 14:52
    find the last digit of 2^2349
  2. 01 Mar '05 17:41 / 3 edits
    2349 = 1 (mod 4)

    2^(4n+1) = 2 (mod 10)

    Therefore last digit of 2^2349 is 2

    In fact, 2^2349 = 131661808029361064474122541992202249544316172470474290896

    938957889657411706431738059855987100606116738608709863898

    114516322696806682779725395040361126073989754846342223650

    752839934282507553095228819445591564242224229100999549808

    158043220482537489286899542806927109262299798576702052364

    647531326323060875437512721666750074735365806697524459192

    563914773873444570420147733289826848369892651509013842153

    766576752759546709772991670483710813378588223114875800405

    103605361303657861719088971021114521028156816509308794659

    625756698728308129465992649969171244954433589856461308546

    917926791439305402526271547340075851639933262085702464422

    986758336147589425826676630311810520418347644992379850195

    840502843574915602317312

  3. Standard member PBE6
    Bananarama
    01 Mar '05 18:19
    Originally posted by THUDandBLUNDER
    2349 = 1 (mod 4)

    2^(4n+1) = 2 (mod 10)

    Therefore last digit of 2^2349 is 2

    In fact, 2^2349 = 131661808029361064474122541992202249544316172470474290896

    938957889657411706431738059855987100606116738608709863898

    114516322696806682779725395040361126073989754846342223650

    752839934282507553095228819445591564242224229100999549808

    1580432 ...[text shortened]... 2

    986758336147589425826676630311810520418347644992379850195

    840502843574915602317312

    Wow. I'm impressed. Any calculator/spreadsheet I've ever used starts throwing up after about 10 number. How did you get all those???
  4. 01 Mar '05 19:40
    Originally posted by PBE6
    Wow. I'm impressed. Any calculator/spreadsheet I've ever used starts throwing up after about 10 number. How did you get all those???
    I used Mathematica.
  5. 02 Mar '05 09:21
    Another good program is Maple.