problem
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
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- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
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- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
Re: problem
ooopppppssss,AntiviruShahriar wrote:
what's the wrong ....my computer is saying that ans will be 4[!!!!!!!!!!]but i can't find any wrong here
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- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
Re: problem
Yaaaahuuu.....
At last ei easy prob taar solution krte paarsi.But aager gulay vul ki chilo???Plz keu b0lo.
$3^{4} \equiv 1$(mod 8)
$3^{2012} \equiv 1$(mod 8)
$3^{2012}-1 \equiv 0 \equiv 8$(mod 8)
$ \frac{3^{2012}-1}{2} \equiv 4$(mod 8)
Ans:4.....
At last ei easy prob taar solution krte paarsi.But aager gulay vul ki chilo???Plz keu b0lo.
$3^{4} \equiv 1$(mod 8)
$3^{2012} \equiv 1$(mod 8)
$3^{2012}-1 \equiv 0 \equiv 8$(mod 8)
$ \frac{3^{2012}-1}{2} \equiv 4$(mod 8)
Ans:4.....
- bristy1588
- Posts:92
- Joined:Sun Jun 19, 2011 10:31 am
Re: problem
Eikhane shamanno ektu shomoshha ase:
Shahriar, TUMI jokhon 2 diye divide korso, tokhon tumi (mod 8) ke divide korte bhule geso.
Shahriar, TUMI jokhon 2 diye divide korso, tokhon tumi (mod 8) ke divide korte bhule geso.
Bristy Sikder
Re: problem
বৃষ্টি ১০০% ঠিক। সহমত।
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
Re: problem
In this case, you just have to notice that,
$8|(3^{4n}+3^{4n+1}+3^{4n+2}+3^{4n+3})$
and so, $8|(3^0+3^1+3^2+3^3..... +3^{2011})$.
Thus the remainder is $0$.
$8|(3^{4n}+3^{4n+1}+3^{4n+2}+3^{4n+3})$
and so, $8|(3^0+3^1+3^2+3^3..... +3^{2011})$.
Thus the remainder is $0$.
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
Re: problem
আরে এটা তো খেয়াল করিনি। তাহলে শাহরিয়ার ভুলটা করল কোথায় ???
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........