wydiwyg Posted October 11, 2005 Share Posted October 11, 2005 How to find the unit digit of (743)^38 which I have found in one of the post here in TM. Any one plz explain.... Quote Link to comment Share on other sites More sharing options...
mishum2000 Posted October 11, 2005 Share Posted October 11, 2005 Is it 9 ? Quote Link to comment Share on other sites More sharing options...
manwiththemission2005 Posted October 11, 2005 Share Posted October 11, 2005 It is 9. (743)^1 > Unit digit =3 (743)^2 > Unit digit = 9 (743*3) (743)^3 > Unit digit =7 (743)^4 > Unit digit = 1 (743)^5 > Unit digit = 3 again.. so the cycle gets repeated . 1,5,9,13,17,21,25,29,33,37.. for those powers.. you get 3 as unit digit. for 38th power, multiply again by 743, you get 9 :) Quote Link to comment Share on other sites More sharing options...
wydiwyg Posted October 11, 2005 Author Share Posted October 11, 2005 Thanks mwm ..nice explanation. Quote Link to comment Share on other sites More sharing options...
seagull Posted October 11, 2005 Share Posted October 11, 2005 gr8 explanation, thanks :) [clap] It is 9. (743)^1 > Unit digit =3 (743)^2 > Unit digit = 9 (743*3) (743)^3 > Unit digit =7 (743)^4 > Unit digit = 1 (743)^5 > Unit digit = 3 again.. so the cycle gets repeated . 1,5,9,13,17,21,25,29,33,37.. for those powers.. you get 3 as unit digit. for 38th power, multiply again by 743, you get 9 :) Quote Link to comment Share on other sites More sharing options...
Prestononline Posted October 11, 2005 Share Posted October 11, 2005 Ya came across similar comparision problem in Downdowndown.net Unit digit of of 123^23 & Unit digit of 23^123 Quote Link to comment Share on other sites More sharing options...
manwiththemission2005 Posted October 11, 2005 Share Posted October 11, 2005 7 , 7 Ans is C Quote Link to comment Share on other sites More sharing options...
wydiwyg Posted October 11, 2005 Author Share Posted October 11, 2005 1> 123^23 Ans: 7 2> 23^123 Ans: 7 Quote Link to comment Share on other sites More sharing options...
kronique Posted October 11, 2005 Share Posted October 11, 2005 hey mwm....awesum method...man u a wizard or something???? where d hell did u learn all this??? :tup: [clap] Quote Link to comment Share on other sites More sharing options...
manwiththemission2005 Posted October 11, 2005 Share Posted October 11, 2005 kronique, I ain't a wizard. :) I m pretty strong in discrete mathematics though.... One suggestion : Keep practicing hard . That's what I keep doin in this forum.Never worry abt the result.Make sure you'r satisfied with ur preparation. Only thro continuous practice, I was able to get the knack of solving problems. All the very best Kronique. Quote Link to comment Share on other sites More sharing options...
kronique Posted October 11, 2005 Share Posted October 11, 2005 thanx mate for d encourangement...................gotta start my prep soon.... best o luck to u too for ur tests!!!:tup: Quote Link to comment Share on other sites More sharing options...
mote Posted October 14, 2005 Share Posted October 14, 2005 743^38 = (743^2)^19 = (....9)^19 Now we know all odd powers of 9 carries unit digit 9 !!! So answer is 9 123^23 = (123^4)^5 * (123^3) = ....1 * ....7 So answer is 5 Quote Link to comment Share on other sites More sharing options...
kronique Posted October 14, 2005 Share Posted October 14, 2005 123^23 = (123^4)^5 * (123^3) = ....1 * ....7 So answer is 5 can u plz explain this...btw the ans. is 7!! Quote Link to comment Share on other sites More sharing options...
mote Posted October 15, 2005 Share Posted October 15, 2005 ya... sorry... answer is 7 Quote Link to comment Share on other sites More sharing options...
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