Search found 230 matches
- Wed Jun 02, 2021 12:07 pm
- Forum: National Math Camp
- Topic: Special Problem Marathon
- Replies: 38
- Views: 34473
Re: Special Problem Marathon
Problem 4: Find all functions $f : \mathbb{Z} \rightarrow \mathbb{Z}$ such that $$f(x + y) + f(x)^2f(y) = f(y)^3 + f(x + y)f(x)^2$$ for all $x, y \in \mathbb{Z}$. Let, $p(x,y)=f(x + y) + f(x)^2f(y) = f(y)^3 + f(x + y)f(x)^2$ Now, by $p(0,0)$ we get, $f(0)+f(0)^3=f(0)^3+f(0)^3$ Or, $f(0)^3-f(0)=0$ E...
- Tue Jun 01, 2021 10:11 pm
- Forum: Astronomy & Astrophysics
- Topic: Do you believe in possibility of life in other galaxies?
- Replies: 10
- Views: 30061
Re: Do you believe in possibility of life in other galaxies?
With a telescope it`s impossible to detect forms of life from other galaxies. But such space missions like James Webb Space Telescope- the most expensive telescope ever or Ariel space telescope can give as a hint at the possibility of existence of other worlds. Both of the projects are aimed at sea...
- Fri May 28, 2021 10:38 pm
- Forum: College / University Level
- Topic: All About Decimals
- Replies: 1
- Views: 6202
Re: All About Decimals
$1.$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{difference}$ $\text{among}$ $\text{‘decimal}$ $\text{number’,}$ $\text{‘decimal}$ $\text{numeral’,}$ $\text{‘decimal}$ $\text{fraction’}$ $\text{and}$ $\text{‘decimal}$ $\text{numeral}$ $\text{system’?}$ $2.$ $\text{Is}$ $\text{decimal}$ $\text{a}$...
- Wed May 26, 2021 12:58 pm
- Forum: College / University Level
- Topic: All About Fractions
- Replies: 5
- Views: 10864
Re: All About Fractions
1) I don't know the formal definition of fractions, but intuitively I know is that fraction is just a way to represent numbers. 2)I think saying that a fraction is $\frac{a}{b}, a,b \in \mathbb{R}$ or $\mathbb{C}$ and $b \neq 0$ is enough to say to make all the fractions possible.(Maybe) 3)In the se...
- Mon May 24, 2021 7:39 pm
- Forum: Social Lounge
- Topic: Struggling with math
- Replies: 6
- Views: 14125
Re: Struggling with math
I suggest that you do Olympiad Math in such a way that will not negatively affect your HSC result. You should focus on HSC. :cry: OK then :( . By the way, how do you guys balance academic and olympiad? Have you guys completed the theory(essential) portion of all 4's and now just practicing? Or, you...
- Sun May 23, 2021 7:14 pm
- Forum: Social Lounge
- Topic: Struggling with math
- Replies: 6
- Views: 14125
Re: Struggling with math
I suggest that you do Olympiad Math in such a way that will not negatively affect your HSC result.
- Tue May 18, 2021 9:21 pm
- Forum: Number Theory
- Topic: A question concerning multiplicative function
- Replies: 2
- Views: 48506
Re: A question concerning multiplicative function
The is a Mobius function in number theory which is stated as, \[ \mu (n)= \begin{cases} 1 & \text{if n=1} \\ 0 & \text{if } p^2 | n \text{ for some prime } p>1 \\ (-1)^k & \text{if } n=p_1 \cdots p_k \text{ where } p_1,\cdots p_k \text{ are distinct primes} \\ \end{cases} \] And it is also said tha...
- Tue May 18, 2021 8:40 pm
- Forum: Number Theory
- Topic: A question concerning multiplicative function
- Replies: 2
- Views: 48506
A question concerning multiplicative function
The is a Mobius function in number theory which is stated as, \[ \mu (n)= \begin{cases} 1 & \text{if n=1} \\ 0 & \text{if } p^2 | n \text{ for some prime } p>1 \\ (-1)^k & \text{if } n=p_1 \cdots p_k \text{ where } p_1,\cdots p_k \text{ are distinct primes} \\ \end{cases} \] And it is also said that...
- Thu May 13, 2021 10:34 pm
- Forum: Social Lounge
- Topic: Eid mubarak
- Replies: 1
- Views: 7064
Re: Eid mubarak
Eid Mubarak Brother
- Thu May 13, 2021 5:22 pm
- Forum: National Math Camp
- Topic: Problem - 01 - National Math Camp 2021 Mock Exam - "Not as bad as it looks"
- Replies: 4
- Views: 6666
Re: Problem - 01 - National Math Camp 2021 Mock Exam - "Not as bad as it looks"
Let $a_1 \leq a_2 \leq a_3 \cdots \leq a_n$ be a sequence of positive integers. For $1 \leq i \leq a_n$, let $b_i$ be the number of terms in the sequence that are not smaller than $i$. It is given that, $b_1 > b_2 > \cdots > b_{a_n}$, for each $1 \leq i \leq a_n, b_i$ is a power of three, and $b_1 ...