Peru Mathematical Olympiad Training

Hi everybody!

I'm Jorge Tipe from Peru, I'm one of the coaches of the Peruvian mathematical team. In Lima, we meet once or twice a week to have lessons and solve some problems. Our group consists of about twelve students, they will represent my country in the different mathematical olympiads such as Cono Sur Mathematical Olympiad, Iberoamerican, Rioplatense and of course IMO. Later I will comment about these olympiads, probably you never heard about some of them.

The idea of #PeruMOTraining is to share with you some material such as

Lessons with solved problems and some additional problems for you. These lessons will be divided in parts I, II, III,... as needed.
Problems or set of problems for training. I will try to use some not well known problems including those of the Peruvian Mathematical Olympiad and the olympiads above mentioned.

Starting for now, I will have new material for you every week!

Jorge.

#PeruMOTraining

Easy Math Editor

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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Aw. Thank you very much sir. I'm so glad that you'll be training us with other teachers too :)

Priyansh Sangule - 7 years, 5 months ago

I can't wait! Here is the link to the first problem! It's a geometry proof :)

Calvin Lin Staff - 7 years, 5 months ago

hi Jorge could you please solve the problem which I reshared a couple of hours ago

Des O Carroll - 7 years, 4 months ago

What problem?

Jorge Tipe - 7 years, 4 months ago

minimum value of z such that z^3 =a^4 +b^4+(a+b)^4 for distinct positive integers a and b sorry for not making that clear Jorge would really love to see a solution to that problem looking forward to hearing from you Des O Carroll

Des O Carroll - 7 years, 4 months ago

@Des O Carroll – The first step is to factorize $a^4+b^4+(a+b)^4=2(a^2+ab+b^2)^2$ . Hope this helps!

Jorge Tipe - 7 years, 4 months ago

@Jorge Tipe – thanks Jorge but I got that far then I considered (a^2 +ab +b^2)^2 =2^8 ; 2^14;2^21etc but got no solution then I considered (a^2 +ab+b^2)^2=2^2.3^6;2^2.3^12 etc at this stage all I want is the answer can you give it to me Thanks Jorge

Des O Carroll - 7 years, 4 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}`	$\boxed{123}$