## Search found 188 matches

Sun Jan 27, 2013 7:29 pm
Forum: Social Lounge
Topic: info.
Replies: 4
Views: 1927

### 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: 2478

### 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: 1558

### Re: Help to prove!

Thanks to inform me about LTE thing!!Thaks a lot !!Here is my first solution using LTE.
$v_{3}(10^{3^{n}}-1)=v_{3}(10^{3}-1)+v_{3}(3^{n-1})=3+n-1=n+2.$
Sat Jan 19, 2013 4:39 pm
Forum: Number Theory
Topic: Help to prove!
Replies: 5
Views: 1558

### 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?
Fri Jan 18, 2013 6:56 pm
Forum: Secondary Level
Topic: নিউরনে অনুরণন থেকে...
Replies: 6
Views: 9236

### 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: 1447

### 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 $k!(p-k-1)!$.
Mon Dec 24, 2012 7:21 pm
Forum: Secondary Level
Topic: My first posted problem.
Replies: 6
Views: 1991

### 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)
Thu Dec 20, 2012 7:34 pm
Forum: Primary Level
Topic: গনিত নয় ধাঁধাঁ
Replies: 5
Views: 5686

### 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 ?
Wed Oct 24, 2012 5:51 pm
Forum: Junior Level
Topic: Number Theory Aaggainnn...:(
Replies: 10
Views: 4290

### 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: 1633

### 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 $\frac{AR}{A_{1}R}$ ?