Search found 188 matches
- Sun Jan 27, 2013 7:29 pm
- Forum: Social Lounge
- Topic: info.
- Replies: 4
- Views: 4385
info.
জাতীয় গণিত উৎসবে "স্মৃতি পুরষ্কার" কিসের ভিত্তিতে দেয়া হয় কেউ বলতে পারবে?
- Sun Jan 27, 2013 7:12 pm
- Forum: Social Lounge
- Topic: Negative Marking
- Replies: 7
- Views: 5921
Re: Negative Marking
The examiners are not that cruel!
- Sun Jan 20, 2013 4:44 pm
- Forum: Number Theory
- Topic: Help to prove!
- Replies: 5
- Views: 3641
Re: Help to prove!
Thanks to inform me about LTE thing!!Thaks a lot !!Here is my first solution using LTE.
$v_{3}(10^{3^{n}}-1)=v_{3}(10^{3}-1)+v_{3}(3^{n-1})=3+n-1=n+2.$
$v_{3}(10^{3^{n}}-1)=v_{3}(10^{3}-1)+v_{3}(3^{n-1})=3+n-1=n+2.$
- Sat Jan 19, 2013 4:39 pm
- Forum: Number Theory
- Topic: Help to prove!
- Replies: 5
- Views: 3641
Help to prove!
A number is made with $3^{n}$ same digit.Prove that it is divisible by $3^{n}$ .
(Example:$3 \mid 888$,$9\mid222222222$.)
That is, we have to prove that $10^{3^{n}}\equiv1(mod3^{n+2})$.But how?
(Example:$3 \mid 888$,$9\mid222222222$.)
That is, we have to prove that $10^{3^{n}}\equiv1(mod3^{n+2})$.But how?
- Fri Jan 18, 2013 6:56 pm
- Forum: Secondary Level
- Topic: নিউরনে অনুরণন থেকে...
- Replies: 6
- Views: 15818
নিউরনে অনুরণন থেকে...
Find all natural $n$ for which,$\frac{2^{n}+1}{n^{2}}$ is an integer.
- Sat Dec 29, 2012 5:35 pm
- Forum: Secondary Level
- Topic: Binomial Residue
- Replies: 4
- Views: 3266
Re: Binomial Residue
$(p-1)!\equiv(p-1)(p-2)(p-3)...(p-k)(p-k-1)!\equiv(-1)^{k}k!(p-k-1)!(modp)$
As p is odd prime,$gcd(p,k!(p-k-1)!)=1$.So we can divide both side of the equation by $k!(p-k-1)!$.
As p is odd prime,$gcd(p,k!(p-k-1)!)=1$.So we can divide both side of the equation by $k!(p-k-1)!$.
- Mon Dec 24, 2012 7:21 pm
- Forum: Secondary Level
- Topic: My first posted problem.
- Replies: 6
- Views: 4488
Re: My first posted problem.
I think the answer isn't unique (probably!!).Because, doing the same thing over a small set of numbers(say 1,2,3,..6)
doesn't give an unique answer.
doesn't give an unique answer.
- Thu Dec 20, 2012 7:34 pm
- Forum: Primary Level
- Topic: গনিত নয় ধাঁধাঁ
- Replies: 5
- Views: 11568
গনিত নয় ধাঁধাঁ
পাঁচটি সংখ্যা থেকে (ধনাত্মক বা ঋণাত্মক দুই-ই হতে পারে) তিনটি করে সংখ্যা নিয়ে যোগ করলে যোগফলগুলো হল :
$0,3,4,8,9,10,11,12,14,19$. সংখ্যাগুলো কী কী ?
$0,3,4,8,9,10,11,12,14,19$. সংখ্যাগুলো কী কী ?
- Wed Oct 24, 2012 5:51 pm
- Forum: Junior Level
- Topic: Number Theory Aaggainnn...:(
- Replies: 10
- Views: 8162
Re: Number Theory Aaggainnn...:(
Yes,It is...We have to use all the digits and exactly once.
- Tue Oct 23, 2012 7:21 pm
- Forum: Secondary Level
- Topic: Seems easy
- Replies: 4
- Views: 3476
Re: Seems easy
Sorry,but pls clarify what is meant by "ratio of intersection".If the intersection point is $R$,then what the question asks, $\frac{CR}{C_{1}R}$ or $\frac{AR}{A_{1}R}$ ?