Turkish Junior Mathematical Olympiad 2013 Problem 2

#MathOlympiad #Primes #NumberTheory
The International Mathematical Olympiad 2020 was just held last week.
See how I solved one of the problems in 7 minutes!!
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Link: / lets.think.critically
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I share Maths problems and Maths topics from well-known contests, exams and also from viewers around the world. Apart from sharing solutions to these problems, I also share my intuitions and first thoughts when I tried to solve these problems.
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[@makmesanovic8568]

You are back at making videos! So hyped to be honest, I'm gonna drop a like before watching I know it will be great!

[@letsthinkcritically]

Yes, have been busy over the past month. More videos in the making!

[@chhabisarkar9057]

Back after a long time !

[@ravinderbhandari1974]

you're back woohooo, lets go my g, amazing video. hope your work pays off

[@letsthinkcritically]

Yes, have been busy over the past month. More videos in the making!

[@pedrojose392]

Good evening! Congratulations for this breathtakling beuatiful solution! I have no words to discribe, even if it was in my native language. For videos like that, it should be allowed to give at least 5 likes for each person.

[@arpangoswami5760]

I was able to reduce the equation to q⁴-4q³+q²+19=r² but didn't know the bounding trick.

[@bimalpal573]

Please continue making more videos like this

[@AlephThree]

For the bounds, how do you come up with the number to use at the end of the expression (in brackets that you’re squaring)? Thanks

[@miguelbustamante5271]

q^4-4q^3 is present in the expansion of (q^2-2q)^2, so it is natural to compare it to the squares of numbers similar to q^2-2q (in this case, substracting 1 or 2 since tha particular square is larger than the quartic expression).

[@bimalpal573]

Sir it would also be very great of you to upload some theory lectures on geometry and u equalities. It would be very nice. As I don't get anything about such complex constructions

[@mcwulf25]

Rather complicated for a junior Olympiad. The bounding trick took some understanding. Still need to convince myself how to apply it.

[@VerSalieri]

This is my third video I watch on your channel. The first two were great. The content always is.. but this one was not very enjoyable. The reason is, the rate at which humans write is approximately the same rate at which we absorb information, and you can adjust your rate of speech accordingly. So when you write while explaining, it all sinks in and works perfectly. But here, when you just smack some calculations on the screen and talk through it, I find myself torn between trying to follow your voice and the displayed information, which takes me out of sync. So I hope in your other videos, I find you writing down the solutions or at least revealing the calculations bit by bit. Note: I had the same problem with my students last year (last academic year I mean) when we tried online teaching. Anyway, I am enjoying your content so far. Good work my friend, and forgive my criticism..

[@letsthinkcritically]

Thank you for your detailed feedback!! I have been struggling to present my thoughts without boring the audience too much, and I found a very convenient app that made things easier. The most recent video returns to the ‘write-as-i-speak’ format, and I plan to go for that in future videos too. Do check it out and I hope you like it!

[@VerSalieri]

@@letsthinkcritically Oh I absolutely loved your channel and subbed from my second video, which is why I tried reaching out with my feedback.. always on the lookout for math channels that present content in a concise manner. Thanks for taking my feedback seriously.

[@bimalpal573]

Sir you are the best

[@ravinderbhandari1974]

hey man, even though this is great quality, your handwritten videos were great too as they added the humanly feeling and i think they may be easier to produce so pls don't try to stress over presentations and shit, just focus on MATH

[@letsthinkcritically]

I have been experimenting on various ways to present my thoughts (still new to making Maths videos). To be honest it’s quite hard to write nicely as I speak. I will try to make future videos feeling more humane 😄

[@ravinderbhandari1974]

@@letsthinkcritically oh no don't get me wrong, this feels great. i just thought it would be easier for you to write as i see a lot of math channels saying that making presentations is hard. i come for the math, i think most people don't care about fancy 'presentation' so you should do what you find easy. cheers

[@thayanithirk1784]

Please provide solution for this question sir;prove that( 3^n+2) does not divide (2^3^n)+1

[@letsthinkcritically]

At first glance I think this can be done by Induction.

[@thayanithirk1784]

letsthinkcritically please make a vedio on it sir

[@kshitij5865]

You can take both sides modulo 3 and notice that RHS is divisible by 3 while the left side is not for all n>0

[@TheodoreBrown314]

@@kshitij5865 I don't think that works. 2^3^n = 2^(3^n), and (2^odd) + 1 is always divisible by three

[@thayanithirk1784]

Thank you for uploading the vedio for my request,can you please upload theory lectures

[@letsthinkcritically]

My pleasure to share Mathematics around! Feel free to suggest other problems for future videos!

[@jayachandranthuwaragesh4797]

do u solve problems proposed/ requested by viewers?

[@ravinderbhandari1974]

Are you participating in these math olympiads too?

[@letsthinkcritically]

Yes, I participated a few national level contests when I was a student.

[@ravinderbhandari1974]

@@letsthinkcritically so do you go to a college now?

[@letsthinkcritically]

I am now a Maths schoolteacher

[@ravinderbhandari1974]

@@letsthinkcritically oh wow you seemed really young so i thought you would still be in school lol

[@boraolmez6622]

I have two questions: 1) Do you participate in Olympiads (or have u participated)? 2) Are u Turkish? because most of the problems I present are from TJMO....

[@boraolmez6622]

U present*

[@letsthinkcritically]

I have participated national-level olympiad contests when I was a student. I am actually from Hong Kong. Feel free to suggest problems that you want me to talk about!

[@alainrogez8485]

I don't understand very well your "explanations". I think you should have written when you were explaining. Moreover, some of your tricks came from nowhere.

[@kikiak4971]

hi. nice video. can anybody see my comment. I posted a comment on other videos. but i can't see it

[@xriccardo1831]

I like the bashy problems