DIGIT
Forum rules
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.
-
- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
-
- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
-
- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
Re: DIGIT
hide অংশ টা দেখেছ ভাইয়া??? $1000$ কে আমি সরাসরি বাদ দিয়েছি...। আমার উত্তর টা ঠিক আছে???tushar7 wrote:NOTE that $1000=8.125$
-
- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
Re: DIGIT
binomial থেকে $(1000+2)^x$ $\equiv$ $2^x$
কারণ, $1000($ শেষ পদ বাদে বাকি পদ$)+2^x$.
কারণ, $1000($ শেষ পদ বাদে বাকি পদ$)+2^x$.
-
- Posts:125
- Joined:Mon Dec 13, 2010 12:05 pm
- Location:চট্রগ্রাম,Chittagong
- Contact:
Re: DIGIT
$2^{10}$ $\equiv$ $24$ $\equiv$ $3 \cdot 2^3$ $(mod 1000)$........................[1]
$2^{40 \cdot 5} \cdot 2^{10}$ $\equiv$ $776^5 \cdot 24$ $(mod 1000)$.
$2^{210}$ $\equiv$ $1024$ $(mod 1000)$.
$2^{209}$ $\equiv$ $1024 \cdot \frac{1}{2}$ $(mod 1000)$.
Ans: $512$.............[$2^{40}$ ta alada vaabe bair korsi...]
$2^{40 \cdot 5} \cdot 2^{10}$ $\equiv$ $776^5 \cdot 24$ $(mod 1000)$.
$2^{210}$ $\equiv$ $1024$ $(mod 1000)$.
$2^{209}$ $\equiv$ $1024 \cdot \frac{1}{2}$ $(mod 1000)$.
Ans: $512$.............[$2^{40}$ ta alada vaabe bair korsi...]