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actually writing solution is a completely different muscle to build aside from problem solving. For this I think the best way is to read other's(experienced) solutions.For example sometimes you have vague idea that solves the problem (especially in combii) but to write it in the language of math it ...

One of the cute dio i have seen Solution: we claim that the only solution is $(m,n)=(3,2)$ Case 1: $ m \geq n$ Observe $V_2(n)=V_2(m!) \geq V_2(n!)$ $\Rightarrow V_2(n) \geq V_2(n!)$ It is easy to see $n=2$ is the only solution to this inequality. Case2: $m<n$ Observe $2^m+n<m!;2^n+m<m!$ $\Rightarro...

May Allah SWT make this day blessed for us and accept our deeds.

Need some suggestions
1.What is the best way to learn and excel at it?
2.What are some beginners book or resource to start with?
3.Planning to start with C as our intermediate syllabus also includes it.

Solution(expected solve with coloring a solution with coloring would be generous :oops: still afraid that this may be a fakesolve ) Update: It is a partial solve i.e half solved :cry: :cry: (Trying to fix it :x) Denote the small rectangles as sub-rectangles and their sides be $a_i$ and $b_i$ also le...

C1
A rectangle R with odd integer side lengths is divided into small rectangles with integer
side lengths. Prove that there is at least one among the small rectangles whose distances from
the four sides of R are either all odd or all even.

Acceleration is the second derivative of position with respect to time. The position of the object is given by, $y(t)=v_0t-\frac12gt^2$ $\Rightarrow y''(t)=-g$ Some confusion is arising that since the object was moving upwards, there should be an upward force acting on that object, and the gravitat...

For HSC first year in the first week (surely everybody has submitted that by now) there was a problem stating: What is the acceleration of a vertically thrown object at the peek of its path? Somebody say it is $0ms^{-2}$ some say it is $9.8ms^{-2}$ I am on the side of $9.8ms^{-2}$ here is my reason:...

Almx26 wrote: ↑

Wed Jun 02, 2021 8:35 am

An infinite series of integers follows the following rule:
$a_{n+1}=2a_n +1$
Is there any $a_0$ for which every term of the series will be a prime number?

Is there any recipe to cook prime numbers?

Let's imagine a big rectangle $ABCD$ (named in clockwise direction) inside of which a closed loop is lying. Now start moving the side $AB$ towards $CD$ until it touches the closed loop. Do this for every sides, pull them towards the opposite side until they touches the loop. Following this algorith...