Перезапуск Теории чисел. Основная теорема арифметики

Watch on BOBR: https://bobr.video/watch/316a72b3-b5c... Materials: https://t.me/DA_shkolkovo/3896 🔥 We've launched sales of annual subscriptions for List 26/27. Join the training using the promo code 🔥LET'S GO🔥 for a 20% DISCOUNT and get free access to last year's course: https://3.shkolkovo.online/olymp-math... Subscribe to Dmitry Alekseevich's Telegram: https://t.me/DA_shkolkovo ✅ Free pre-course "Olympiad Base-2026" for those who want to start preparing for the competition from scratch Olympiads: https://3.shkolkovo.online/olymp-base... ✅ We've launched sales of annual plans for the VsOSH course for grades 26/27. Join the preparation with a 20% discount using the promo code 🔥REGION🔥 and get full access to the 25/26 course for free🎁, including written homework checks and auditions according to your chosen plan: https://3.shkolkovo.online/vsosh?utm_... ✅ Advanced and Olympiad Mathematics for grades 8-9: https://3.shkolkovo.online/olymp-math... All our current promotions and discounts👉🏻 https://3.shkolkovo.online/special?ut... Feedback from our students👉🏻 https://3.shkolkovo.online/reviews?ut... VK group on Olympiad Mathematics 👉🏻https://vk.com/perechenolymp 00:00 – Pam-pam-pam, hello everyone! 01:45 – What do we know about factorization? Let's review prime numbers, their properties, and the fundamental theorem of arithmetic. 09:10 – Problem 1. How are a cube and a square represented in prime factorization? Let's solve the problem without trying. 27:40 – Problem 2 [MMO, 2009, 10.1]. Let's look at percentages and factorization. Don't forget to reread the problem statement to answer the question correctly. 43:30 – Problem 3 [Interved, 2024, 11.1]. Why is it interesting that the numbers are consecutive? We can guarantee that the product is definitely divisible by some factors. Can we solve it using combinatorics? 54:10 – Problem 4. Is this a problem about solid geometry in number theory!? The only geometry required is the ability to draw a cube! 1:07:10 – Problem 5 [OMMO, 2016]. We calculate the sum of an arithmetic progression without using a formula and again look at the factorization of the factors. 1:29:00 – Problem 6. What is a large number? We'll consider adjacent factorials and look for squares!