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Last digit problem

how to solve this please give a solution for it i have found it on internet \({ 7 }^{ { 7 }^{ { 7 }^{ 7... } } }(2008\quad 7's)mod(13)\) and also its last digit

Note by Rishabh Jain
2 years, 9 months ago

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oh god !! so much discussion but no proper solution ?? Rishabh Jain · 2 years, 9 months ago

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@Rishabh Jain i got the last digit but not mod13 part Rishabh Jain · 2 years, 9 months ago

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@Rishabh Jain Hi! Well, you can do this easily too! Come-on! Write the rem's obtained when 7 power 1-12 are divided by 13. You will find the numbers 1-12 are cycled. Simply plug-in the value of rem\(7^{7}\) from there. That's all. Is 6 correct? Tell me where you got this from also! Please!!!!! Krishna Ar · 2 years, 9 months ago

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@Rishabh Jain Hey! You should see my comment below! It explains everything. If you still dont get it, please tell me...I will post the whole solution. And ,could you tell me the source of this problem pleasE? Krishna Ar · 2 years, 9 months ago

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hey @Finn Hulse @Sharky Kesa @Krishna Ar or anyone please answer it !! Rishabh Jain · 2 years, 9 months ago

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@Rishabh Jain Whoa! Thanks for tagging me here @Rishabh Jain . Well the answer is that the expression is 6 mod 13 and also 3 mod 10 (last digit). Tell me if its right, if yes, I shall very soon post a full solution. I can perhaps give a small hint that you must analyse the remainders obtained on divison of powers of 7 by 13 till u get a pattern/chain. Or plug in euler :p Krishna Ar · 2 years, 9 months ago

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@Krishna Ar Ur answer is correct krishna. ...All hail euler :D Poonayu Sharma · 2 years, 9 months ago

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@Poonayu Sharma :D HOW R YOU SO SURE? . I didnt use totient though Krishna Ar · 2 years, 9 months ago

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@Krishna Ar I used totient to find last digit ..but still I am confused on how to deal with the 7^7 2008 times mod 13 part ...can u please give a hint :) Poonayu Sharma · 2 years, 9 months ago

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@Poonayu Sharma Hint is above in the previous comment. Krishna Ar · 2 years, 9 months ago

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@Krishna Ar Got it....but don't u think that it's a long process ....isn't there a shorter way ? Poonayu Sharma · 2 years, 9 months ago

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@Poonayu Sharma Know wut? It is not long at all, I did it in some 45 secs! Srsly! No kiddin' Krishna Ar · 2 years, 9 months ago

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@Krishna Ar Did u use eulers criterion too ? I tried using it ...I also got it in 45 sec Poonayu Sharma · 2 years, 9 months ago

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@Poonayu Sharma No Krishna Ar · 2 years, 9 months ago

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@Krishna Ar Well..y don't u post ur solution :/ Poonayu Sharma · 2 years, 9 months ago

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@Poonayu Sharma Gosh! Please see the very first comment of mine! Krishna Ar · 2 years, 9 months ago

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