Search found 107 matches
- Thu Dec 18, 2014 2:34 pm
- Forum: Social Lounge
- Topic: Asking for a book
- Replies: 3
- Views: 3944
Re: Asking for a book
You may also see Geometry Unbound, available on the internet. I think its a great book.
- Mon Nov 10, 2014 7:06 pm
- Forum: Number Theory
- Topic: Perfect Square ratio
- Replies: 5
- Views: 5879
Re: Perfect Square ratio
The reasoning falls apart if $ x $ is greater than $ y $.
- Fri Nov 07, 2014 7:59 pm
- Forum: Number Theory
- Topic: NT from Vietnam 2005
- Replies: 3
- Views: 3386
Re: NT from Vietnam 2005
Why?n=0 is impossible.
Again why?$x,y,n>0$
- Wed Nov 05, 2014 10:49 am
- Forum: Number Theory
- Topic: NT from Vietnam 2005
- Replies: 3
- Views: 3386
NT from Vietnam 2005
Find all nonnegtive integer solutions to $\dfrac{x!+y!}{n!}=3^n$
- Tue Oct 28, 2014 10:16 am
- Forum: Secondary Level
- Topic: Floor sum
- Replies: 1
- Views: 2479
Floor sum
Given for a natural number $n$, $\lfloor\sqrt n\rfloor=a$, express $\sum\lfloor\sqrt k\rfloor$ in terms of $n$ and $a$, where $k$ ranges from $1$ to $n$.
- Wed Oct 22, 2014 8:16 pm
- Forum: Secondary Level
- Topic: Functional divisibility
- Replies: 3
- Views: 3889
Re: Functional divisibility
Actually that would be $1988$ instead of $1998$. Corrected now. And I think it would be relevant to cite the source of this problem. its from Chinese TST 1988.
- Tue Oct 21, 2014 11:04 pm
- Forum: Secondary Level
- Topic: Functional divisibility
- Replies: 3
- Views: 3889
Functional divisibility
Given $f(n)=3n+2$, prove that there exists a natural number $n$ such that $f^{100}(n)$ is divisible by $1988$.
- Sat Oct 18, 2014 10:25 am
- Forum: Number Theory
- Topic: Again Sum with floor
- Replies: 0
- Views: 1919
Again Sum with floor
Let $p$ be an odd prime and $q$ be a positive integer that is not divisible by $p$. Show that
\[\sum_{k=1}^{p-1} \left\lfloor (-1)^k\cdot\frac{k^2q}{p}\right\rfloor=\frac{(p-1)(q-1)}{2}\]
\[\sum_{k=1}^{p-1} \left\lfloor (-1)^k\cdot\frac{k^2q}{p}\right\rfloor=\frac{(p-1)(q-1)}{2}\]
- Fri Oct 17, 2014 3:58 pm
- Forum: Higher Secondary Level
- Topic: power and factorial
- Replies: 7
- Views: 6832
Re: power and factorial
Ok but how could it possibly be algebra, Mahi vai ?
- Wed Oct 15, 2014 8:46 pm
- Forum: Higher Secondary Level
- Topic: power and factorial
- Replies: 7
- Views: 6832
Re: power and factorial
You sure?