Chinmay Sangawadekar's Messageboard.

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Life is strong but yet fragile. It's a paradox. It's both things, like quantum physics:It's a particle and a wave at the same time!

#Physics #Space #Mathematics #Life #Chinmay

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

The first and most sensible question:-

Do you like carrots?

Mehul Arora - 5 years, 11 months ago

not really,tell me do you like carrots?

A Former Brilliant Member - 5 years, 11 months ago

Hey Mehul , do you have quadro phobia?

A Former Brilliant Member - 5 years, 11 months ago

Hello Everyone!!!

A Former Brilliant Member - 5 years, 11 months ago

Hello!

Yoogottam Khandelwal - 5 years, 11 months ago

Hey

A Former Brilliant Member - 5 years, 11 months ago

Can you help me out with this?

Yoogottam Khandelwal - 5 years, 11 months ago

Do you like carrots?

Agnishom Chattopadhyay - 5 years, 11 months ago

I too have great interest in quantum physics and relativity .Keep eating carrots like Nihar because you too have the same number of letters in your name as is in carrots.I hope that you might solve the conflict of gravity and quantum mechanics in future.

Siddharth Singh - 5 years, 11 months ago

so you want to do career in pure physics or something else?

A Former Brilliant Member - 5 years, 11 months ago

It is very difficult for me to answer this question because of my wide range of interest in subjects of Mathematics,Physics,Computer Science and Astronomy.

Siddharth Singh - 5 years, 11 months ago

which subject do you like other than mathematics and physics.

A Former Brilliant Member - 5 years, 11 months ago

Computer Science and Astronomy.

Siddharth Singh - 5 years, 11 months ago

Bonne journee is not literally used as 'good day' in francais. It's more like have a good day. Sorry to ruin it. :3

And potato or potato?

Kunal Verma - 5 years, 11 months ago

Got it thanks for that bro .Actually i am learning German not french

A Former Brilliant Member - 5 years, 11 months ago

(http://shivamani patil)

A Former Brilliant Member - 5 years, 11 months ago

Chinmay Sangawadekar

A Former Brilliant Member - 5 years, 7 months ago

Sorry I was practicing to make the link . The blue one...

A Former Brilliant Member - 5 years, 7 months ago

I wanted to spam :P

Nihar Mahajan - 5 years, 7 months ago

Please as you are a moderator do check this problem. Chinmay Sangawadekar

A Former Brilliant Member - 5 years, 7 months ago

@A Former Brilliant Member – Formatting is alright.

Nihar Mahajan - 5 years, 7 months ago

Still it is not getting the rating.

A Former Brilliant Member - 5 years, 7 months ago

@A Former Brilliant Member – Be patient , it will get rated as more and more people view it. If you have a valid reason for urgency for rating it , please tell .

Nihar Mahajan - 5 years, 7 months ago

@Chinmay Sangawadekar, i see that you have interest in contributing to wikis like multiplicative functions and mobius function. talk to me at slack so we could make the wiki better.

Aareyan Manzoor - 5 years, 5 months ago

Brother , I have no access to slack , when I try , it says you are already invited , but I had deleted my emails already :( is there another way to communicate ? On Facebook ? @Aareyan Manzoor

A Former Brilliant Member - 5 years, 5 months ago

Aareyan Manzoor - 5 years, 5 months ago

@Aareyan Manzoor – How is it ? @Aareyan Manzoor

A Former Brilliant Member - 5 years, 5 months ago

@A Former Brilliant Member – oh yes that is cool... back to the topic of sections now. lets decide that what section are required for the wiki?

Aareyan Manzoor - 5 years, 5 months ago

@Aareyan Manzoor – First intro. then theorem(definition) then proof(if necessary) (examples)

A Former Brilliant Member - 5 years, 5 months ago

@Aareyan Manzoor – i enter my email and pass and got Sorry, you entered an incorrect email address or password.

Dev Sharma - 5 years, 5 months ago

@Dev Sharma – Yeah same here , @Dev Sharma

A Former Brilliant Member - 5 years, 5 months ago

https://crypto.stanford.edu/pbc/notes/numbertheory/mult.html , do check this out , it has many useful things which we can use for wiki

A Former Brilliant Member - 5 years, 5 months ago

cool, just went through it.... i was planning to include those sums....

Aareyan Manzoor - 5 years, 5 months ago

@Aareyan Manzoor – Yeah those are really awesome , so i have a plan , I will provide you with the stuff ,you select it and then tell me , then we will add those on wiki

A Former Brilliant Member - 5 years, 5 months ago

@A Former Brilliant Member – ok.. that is a good plan... it is going to become overcrowded your message board. try facebook. i have the same username as brilliant (aareyan manzoor).

Aareyan Manzoor - 5 years, 5 months ago

@Aareyan Manzoor – Sure I will add you immediately

A Former Brilliant Member - 5 years, 5 months ago

@Chinmay Sangawadekar, lets talk about multiplicative function wiki first.

Aareyan Manzoor - 5 years, 5 months ago

okay ,

A Former Brilliant Member - 5 years, 5 months ago

go here for the wiki. what level audience do we target?

Aareyan Manzoor - 5 years, 5 months ago

@Aareyan Manzoor – I think we should aim for high level audience

A Former Brilliant Member - 5 years, 5 months ago

@A Former Brilliant Member – same in my mind. how 'bout lvl 3-5?

Aareyan Manzoor - 5 years, 5 months ago

@Aareyan Manzoor – Sure , first we will make it for level 3-4 then we will ask Calvin Lin for guidance , then we go for advance

A Former Brilliant Member - 5 years, 5 months ago

@A Former Brilliant Member – ok. the sections of the wiki then... how are we going to divide it?

Aareyan Manzoor - 5 years, 5 months ago

@A Former Brilliant Member – now what sections are we going to divide the wiki in?

Aareyan Manzoor - 5 years, 5 months ago

@Otto Bretscher , I wanted ask you about this

Does this mean , that $n^{2015$ }=1 , ?

A Former Brilliant Member - 5 years, 5 months ago

Yes, "primitive root of unity" means that 2015 is the smallest positive integer $k$ such that $\omega^k=1$ .

Otto Bretscher - 5 years, 5 months ago

@Otto Bretscher , can you tell me a general formula to find the product of totient of divisors of any number n

A Former Brilliant Member - 5 years, 5 months ago

@Isaac Buckley why did you choose Computer Sci. topic for this problem of yours ?

A Former Brilliant Member - 5 years, 4 months ago

Can you solve it using number theory?

Aareyan Manzoor - 5 years, 4 months ago

I dont know but problem looks like NT problem. Can you solve it by NT any tries ?

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – I'm not going to say you can't... but if anyone could... they would be a God in the eyes of mathematicians.

Isaac Buckley - 5 years, 4 months ago

@Isaac Buckley – Oh yeah there is no specific formats for primes iant it?@Isaac Buckley

A Former Brilliant Member - 5 years, 4 months ago

I'd love to see anyone try to solve it with number theory, a great prize awaits them.

Isaac Buckley - 5 years, 4 months ago

@Isaac Buckley – M primes are so hard to find using comp. sci, i dont think number theory is the right approach!

Aareyan Manzoor - 5 years, 4 months ago

@Isaac Buckley – Really , well is there any generelization for primes,in such form ? @Isaac Buckley

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – this

Aareyan Manzoor - 5 years, 4 months ago

@A Former Brilliant Member – Well I'm not sure what you mean by that exactly. $2^n-1$ is a possible prime only if $n$ is prime. That's all I can say about this form.

Something you might be interesting in reading up on is Mills' constant. It's a way to find primes. It has major short comings though, still interesting.

Isaac Buckley - 5 years, 4 months ago

@Isaac Buckley – Yes, but mills constant is hard to use as we need to have a good degree of acuracy!

Aareyan Manzoor - 5 years, 4 months ago

@Aareyan Manzoor – Exactly! But it's still amazing that such a constant exists. It's also not known if it rational or not.

Isaac Buckley - 5 years, 4 months ago

@Isaac Buckley – It is suprising how many numbers are yet to be proven irrational. for example $e+\pi$ is not proven to be irrational.

Aareyan Manzoor - 5 years, 4 months ago

@Aareyan Manzoor – Yeah, I love problems like that. I might actually post a problem relating to $e+\pi$ later tonight. It came up in a past exam paper I took. If mills' constant was rational the implications could be pretty big, you could possibly (by magic) find its exact fraction and thus generate as many primes as you want.

Isaac Buckley - 5 years, 4 months ago

@Isaac Buckley – Cool, maybe then someone might use it to prove the riemenn hypothesis!

Aareyan Manzoor - 5 years, 4 months ago

@Aareyan Manzoor – Is it like that ?

A Former Brilliant Member - 5 years, 4 months ago

@Isaac Buckley – Oh yes I agree with Aareyan, and thanks for the link.btw dont forget to try my problems and sorry for self advertising .;)

A Former Brilliant Member - 5 years, 4 months ago

@Isaac Buckley – You there ?@Isaac Buckley

A Former Brilliant Member - 5 years, 4 months ago

@Isaac Buckley – Is $2^n - 1$ a sure prime or is it not sure for prime $n$ ? @Isaac Buckley

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – Only 49 n's have been found such that $2^n-1$ iss prime..... so no!

Aareyan Manzoor - 5 years, 4 months ago

@Aareyan Manzoor – Oh thanks for that info ..

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – It's just a prime candidate. Try and prove that if n is composite then $2^n-1$ is also composite.

Isaac Buckley - 5 years, 4 months ago

@Isaac Buckley – sure ,

A Former Brilliant Member - 5 years, 4 months ago

I didn't, I chose number theory which was then changed to computer science by a moderator. I do not contest to it, it fits well in computer science.

Isaac Buckley - 5 years, 4 months ago

@Aareyan Manzoor , @Nihar Mahajan , dont you think this is level 5 problem ?Somebody set level 3 for it.

A Former Brilliant Member - 5 years, 4 months ago

It is okay. it doesnt use any hard concepts.

Aareyan Manzoor - 5 years, 4 months ago

see thishttps://brilliant.org/problems/double-polynomials/?group=3Bg9df1xnfS9&ref_id=1094417 shouldnt it be lvl 5 ???

A Former Brilliant Member - 5 years, 4 months ago

I think it must be level 3 only. Also , you must mention what $\phi$ function is.

Nihar Mahajan - 5 years, 4 months ago

Hey @Nihar Mahajan take a look at this I strongly feel that this problem should get level 5 (though it has no advanced concepts)atleast 200 or 195 points.Please do update the seed level.I will be very thankfull to you

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – Done. I think this is harder then the previous ones.

Aareyan Manzoor - 5 years, 4 months ago

@A Former Brilliant Member – @Chinmay Sangawadekar in the future please dont tag mods like this, if a mod comes across a problem he will change the level. By tagging you are bothering them, mods are usually busy.

Aareyan Manzoor - 5 years, 4 months ago

@Aareyan Manzoor see the link of problem

A Former Brilliant Member - 5 years, 4 months ago

@Nihar Mahajan , have you started learning limits ?

A Former Brilliant Member - 5 years, 4 months ago

I have finished it.

Nihar Mahajan - 5 years, 4 months ago

Great What source ? M Prakash notes ? @Nihar Mahajan

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – Calculus will be done in MPA during June-July. But due to curiosity I am learning it on my own.

Nihar Mahajan - 5 years, 4 months ago

@Nihar Mahajan – Hmm , so no school today for you ? @Nihar Mahajan

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – Nope, its saturday.

Nihar Mahajan - 5 years, 4 months ago

@Nihar Mahajan – Well ,also see my level two limits problem ,this @Nihar Mahajan

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – Yes , sure.

Nihar Mahajan - 5 years, 4 months ago

@A Former Brilliant Member – Solved it. @Chinmay Sangawadekar

Nihar Mahajan - 5 years, 4 months ago

@Nihar Mahajan – grt :)

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – Post more limit problems please, thanks :)

Nihar Mahajan - 5 years, 4 months ago

@Nihar Mahajan – Hey why dont you try and solve my NT and Algebra lvl 4-5 problems ?@Nihar Mahajan

A Former Brilliant Member - 5 years, 4 months ago

@A Former Brilliant Member – Why don't you solve my all previous problems? @Chinmay Sangawadekar

Nihar Mahajan - 5 years, 4 months ago

@Nihar Mahajan – I was doing them only I did many of your recent problems @Nihar Mahajan

A Former Brilliant Member - 5 years, 4 months ago

@Nihar Mahajan what is the teamdomain of brilliant on slack ?

A Former Brilliant Member - 5 years, 4 months ago

@Nihar Mahajan you may try this

A Former Brilliant Member - 5 years, 4 months ago

Thanks , I got it :)

Nihar Mahajan - 5 years, 4 months ago

@Nihar Mahajan , can you update my solution number ? I have written 6 and deleted my previous one so , can you do that ? or tell any staff member to do so ?

A Former Brilliant Member - 5 years, 4 months ago

Sorry , I can't do that , you may ask Calvin on his messageboard.

Nihar Mahajan - 5 years, 4 months ago

@Nihar Mahajan , you may also try this

A Former Brilliant Member - 5 years, 4 months ago

@Chinmay Sangawadekar You may try this , this .

Nihar Mahajan - 5 years, 4 months ago

solved ,,sorry ,, saw your comment now ,, Nice problems ..

A Former Brilliant Member - 5 years, 4 months ago

@Nihar Mahajan try these problems ;) 1 , and 2

A Former Brilliant Member - 5 years, 4 months ago

@Abhishek Sinha , Sorry to mention you here , but I wanted to know more about the Mathematics Department of MIT Can I get in there ? What is the process to do so ? Please tell.. Also , what is your PhD topic ?

A Former Brilliant Member - 5 years, 4 months ago

You should apply. The application procedure is publicly available. I am working on Network Control and Information Theory. Good luck!

Abhishek Sinha - 5 years, 4 months ago

@Otto Bretscher : Please see if it is true : We have , $a\equiv 1\mod b$ where , $(a,b)$ are consecutive natural numbers such that , $a> b$ , then , $a^{n}\equiv 1\mod bn$ , this congruence is true .

A Former Brilliant Member - 5 years, 3 months ago

No, this is not correct (unless I misunderstand your statement). As a counterexample, consider $n=2, b=3, a=4$ .

Otto Bretscher - 5 years, 3 months ago

Yeah right,,,btw also try my recent problem More Modular in 2016

A Former Brilliant Member - 5 years, 3 months ago

shuddhabho nandi - 5 years, 3 months ago

@Otto Bretscher sorry to mention you here , but in this problem , I have added 1 to the lambda function , so deno. Won't be 0 ...

A Former Brilliant Member - 5 years, 3 months ago

Are we talking about the Liouville function as usual? That one takes the vales 1 and -1.

Otto Bretscher - 5 years, 3 months ago

@Otto Bretscher

There is no fun in doing Number Theory without you...:(

A Former Brilliant Member - 5 years, 3 months ago

I really don't want to post any more problems... then I have to deal with some of these obnoxious guys when they post solutions. Maybe I will give you some ideas and you can post, Comrade!

Otto Bretscher - 5 years, 3 months ago

I am really sorry , all this has happened because of me ...:( @Otto Bretscher

A Former Brilliant Member - 5 years, 3 months ago

@A Former Brilliant Member – Not at all... you are my best Comrade here, @Chinmay Sangawadekar

Otto Bretscher - 5 years, 3 months ago

@Otto Bretscher can you link me to some solutions like this, sorry if your experience in brilliant is harmed by them.

Aareyan Manzoor - 5 years, 3 months ago

@Aareyan Manzoor – Solutions like what, Comrade?

Otto Bretscher - 5 years, 3 months ago

@Otto Bretscher –

I really don't want to post any more problems... then I have to deal with some of these obnoxious guys when they post solutions.

these solutions posted by obnoxious guys.

Aareyan Manzoor - 5 years, 3 months ago

@Aareyan Manzoor – I don't want to name names, but I think you know the type.

Otto Bretscher - 5 years, 3 months ago

@Otto Bretscher – yes, i think i will go through your profile searching on my own for these guys.

Aareyan Manzoor - 5 years, 3 months ago

@Aareyan Manzoor – Aareyan please take strict actions for people like him...

A Former Brilliant Member - 5 years, 3 months ago

Humble Request: Please don't stop posting problems because of obnoxious guys. You are a crucial part of community and so are your problems. We enjoy your problems very much. If some guys are troubling you by any means , you may report it in private or on message board of any staff and the staff will take the appropriate action. Grooming math enthusiasts and comrades like Chinmay , Aareyan , me need your help on Brilliant , but if you stop posting problems like this for some reason you are not responsible for , we would be discouraged :(

Nihar Mahajan - 5 years, 3 months ago

@Nihar Mahajan – i agree; without his problem i never would have learned abt half the things iknow now, please dont stop otto sir; you are one of the best problem posters here.

Aareyan Manzoor - 5 years, 3 months ago

@Nihar Mahajan – I agree with you aareyan...and Nihar...

A Former Brilliant Member - 5 years, 3 months ago

Oh lord no! Your problems are really integral to the community, sir. Please don't stop posting problems. As Nihar rightly did point out, you may report any such action to the staff, so that appropriate action can be taken. But please don't stop posting problems! :(

Mehul Arora - 5 years, 3 months ago

@Otto Bretscher

Please look into my latest problem , Gauss won't help,, it is getting a lot of reports , but still I think problem may be right...help me comrade...

A Former Brilliant Member - 5 years, 3 months ago

It's great problem and your answer is correct, Comrade. You should write the Legendre symbol more clearly as $\left(\frac{n(n+1)}{10009}\right)$ though

Otto Bretscher - 5 years, 3 months ago

@Otto Bretscher dsorry to disturb you ...https://brilliant.org/problems/more-problems-in-2016-part-11/?group=JgjXt4dJvxew&ref_id=113

A Former Brilliant Member - 5 years, 3 months ago

@Aareyan Manzoor @Sharky Kesa see this problem......

this

A Former Brilliant Member - 5 years, 3 months ago

404 is a palindrome in base: -31

Nihar Mahajan - 5 years, 3 months ago

Check my profile then...

A Former Brilliant Member - 5 years, 3 months ago

@Otto Bretscher

this and this

Kindly see into those problems...They are getting low response and also they are waiting for your awesome solutions...;)

A Former Brilliant Member - 5 years, 3 months ago

Looks like everybody is busy at school or work, including myself ;)

Otto Bretscher - 5 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$