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Many advanced math courses are difficult to teach remotely. For example, how to teach a student to solve complex problems in number theory or methods of rigorous proof if personal communication in class and discussion of the results face- to face are not possible? The author will demonstrate some teaching methods practiced by her in distance learning environment. The presentation will be useful to anyone who wants to help students deeply understand the subject of number theory. Student’s feedback and their results confirm the importance of the proposed teaching method