Tasks here: https://1.shkolkovo.online/public-sto... ➡ Connect for FREE to the Click of the Unified State Exam in Mathematics and get charged with knowledge👇 https://3.shkolkovo.online/shelchok-e... 👀More details about the Click of the Unified State Exam 2024 here: https://3.shkolkovo.online/shelchok-e... Summer vacation as a 🎁 GIFT? Easy! For those who connect to the Time of the First - Summer course is a bonus 👇 🏁Unified State Exam: https://3.shkolkovo.online/vremya-per... 🏁Basic State Exam: https://3.shkolkovo.online/vremya-per... 🏁10th grade: https://3.shkolkovo.online/vremya-per... ❗HURRY UP: the price for VP will increase on June 9th 😱 🎯 Spin the roulette and get an additional discount 👉🏻https://3.shkolkovo.online/fortune?ut... 💸Find out more about how to save money here ⬇ https://3.shkolkovo.online/vozvrat-nd... All our current promotions and discounts 👉🏻 https://3.shkolkovo.online/special?ut... 🤩Feedback from our students👉🏻 https://2.shkolkovo.online/reviews?ut... Telegram channel on mathematics with MO👉🏻 https://t.me/MO_EGE 💥 Subscribe to notifications and mailing of useful materials on VK👉🏻 https://vk.com/app5898182_-185634090#... Our channels: ✔️Olympiad Mathematics with DA: https://shkolkovo.info/yt1 ✔️ Physics with AB: https://shkolkovo.info/yt2 ✔️ Preparation for the OGE for all subjects: https://shkolkovo.info/yt4 ✔️ Social Science with MV: https://shkolkovo.info/yt5 ✔️ Biology with EV: https://shkolkovo.info/yt6 ✔️ Biology and Chemistry Mutagen: https://shkolkovo.info/yt7 ✔️ Easy-USE Mathematics with Ali: https://shkolkovo.info/yt9 ✔️ Mathematics with MO and Russian language with TA (Shkolkovo Main Channel): https://shkolkovo.info/yt10 ✔️ Maxim Koval. Vlog of a math teacher: https://shkolkovo.info/yt11 ✔️ Economics. Shkolkovo Olympiads: https://shkolkovo.info/yt12 ✔️Physics OGE with GK: https://shkolkovo.info/yt13 ✔️History with AB: https://shkolkovo.info/pf ✔️English with SS: https://shkolkovo.info/pg ✔️Computer Science BU: https://shkolkovo.info/tn ✔️Social Science OGE: https://shkolkovo.info/xj 0:00 Plans for the web. Let's review the main topics: invariant, remainders, OTA, arithmetic mean, the idea of ​​​​the minimum sum 6:45 What is an invariant? The first problem is about an invariant and a sequence. We understand the condition, look for an invariant and a solution to item (a). 16:15 First problem. Solution to item (b). 22:30 The sixth problem is about stones. We understand the condition and point (a). 29:45 The sixth problem is about stones. We solve point (b) (we look for an invariant). 41:25 The main theory about remainders, the arithmetic of remainders, parity and divisibility. 1:01:00 The seventh problem is about remainders (numbers are arranged in a circle). We analyze the condition and solve point (a). 1:12:50 The third problem (from the 2023 Unified State Exam). Theory about numbers, how to represent a number. Solution to point (a). 1:23:00 The third problem. Solution to point (b). 1:30:20 The eighth problem (Unified State Exam 2022). We understand the condition and solve point (a). 1:37:00 The eighth problem. We solve point (b). 1:44:25 The fifth problem. Solving point (a) (understanding the condition and trying to construct an example) 1:47:35 Problem 5, point (b). Recalling the remainders and the invariant 1:58:25 Fundamental Theorem of Arithmetic. Any number can be factored into prime factors. 2:03:45 Problem 10. Analyzing the condition (the equiresiduality test) and point (a) 2:14:00 Problem 10, point (b). A beautiful solution using the equiresiduality test 2:18:43 Problem 10, point (b). The second solution method is through factorization and enumeration of possible cases 2:29:10 Break 2:39:10 Continuation of the theory on the Fundamental Theorem of Arithmetic. How can it be used to understand whether a square or a cube can be extracted from a number? 2:45:10 Problem 14 (USE 2019) Solution of item (a) using OTA + recalls the Dirichlet principle 2:58:35 Problem 14. Solution of item (b) 3:09:54 Arithmetic mean. Problem 15. We analyze the condition (introduce unknowns and compose equations) 3:16:54 Problem 15. Solution of item (a) 3:31:05 Problem 15. Beautiful solution of item (b) 3:44:30 Signs of equiresiduality 3:53:10 Problem 18. Solution of item (a). The idea of ​​​​the minimum sum 4:00:00 Drawing