I'm eager to study some advanced topics in Number Theory, of special interest would be applying them to Olympiad problems. If anyone can recommend me some resources for learning and training, it will be a real pleasure. If I find something considered of interest, I also will share it.

What do I consider as advanced topics? First of all use of complex numbers, like Quadratic Extensions and other related topics, also of great interest would be usage of p-adic numbers, anything that will imply usage of abstract algebra, in particular Dirichlet L-functions and Finite Field Extensions.

If anyone got something interesting related to the topics listed above, please answer.

**P.S.** I'm not sure if Brilliant allows it, but feel free to contact me at nikolshapoval at gmail dot com. If it is against the rules, please let me know and I will remove this part.

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how important is it to apply the advanced techniques to Olympiad-level problems?If your answer is "very", you may be in for some disappointment since only very rarely do these techniques offer additional insight. A notable example I can recall is IMO 2008 Q3, Some more examples are given here but generally, such cases are scarce.

If you'd like to learn advanced topics on their own merit, then there's little choice but to follow the long arduous road of learning group theory, rings, fields, commutative rings, before embarking on algebraic number theory.

[ That being said, it's possible to learn unique factorization of "small" quadratic rings (e.g. ring of Gaussian integers) on a very rigourous basis without going into deep mathematics. ]

For p-adic numbers, you have to learn analysis and topology as well because the construction relies on a completely new idea of "distance" (technical term: metric) on the set of rational numbers.

Finally, I've some notes which may be relevant to what you're asking for, but not sure how to share my notes on Brilliant. Anyone knows? – C Lim · 4 years, 2 months ago

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– Shivang Jindal · 4 years, 2 months ago

Can you share it to me too? My email id is shivangjindal@live[dot]comLog in to reply

It would be of great help if you would share your notes via Dropbox or e-mail/Google Drive. Thank you again for assistance. – Nicolae Sapoval · 4 years, 2 months ago

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But I really hope to upload them here so that more students can read them; also any mistakes can be pointed out. – C Lim · 4 years, 2 months ago

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Gaussian Integers, and will continue to build them out as I cover more basics. – Calvin Lin Staff · 4 years, 2 months ago

You can send your notes to me, and I'd look at incorporating them onto the site. I started out developing some theory onLog in to reply

Hope it's of use. – C Lim · 4 years, 2 months ago

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email ID- vcpranav@yahoo.com – Pranav Chakravarthy · 4 years, 2 months ago

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– Anoopam Mishra · 4 years, 2 months ago

Sir, can you please email it to me too? Email ID - mishraanoopam@yahoo.comLog in to reply

– Neelay Trivedi · 3 years, 8 months ago

Could you email the notes to me, my email is trivneel211@gmail.comLog in to reply

– Akshat Jain · 4 years, 2 months ago

Can you email them to me too, sir? Here's my email ID- akshatjain0205@yahoo.co.inLog in to reply

– Superman Son · 4 years, 2 months ago

sir can u please give me the notes id is d_bhattacharia@rediffmail.comLog in to reply