last digit

find the last digit of 2^2349

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

😛

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???

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.

Another good program is Maple.