【高校数学】今週の整数#8【合同式の割り算】

Corrections: 7:40 I think this explanation may have been misleading, so let me clarify. For example, 8 and 5 + 11 are not relatively prime, but 8, 5, and 11 share no common factors other than 1. In other words, even if a number on the right side has no common factors, it can still be relatively prime to the number on the left (a pattern in which a common factor is only created when the numbers are added). The key difference between 8 and 8 + 9 in this case is that the 8 on the right side also has factors other than 1, such as 2, 4, and 8 (the only factors that can divide the left side). In this case, if the numbers are not relatively prime, then the other number on the right side, 9, should also be divisible by 2, 4, and 8. However, since 8 and 9 are relatively prime, this is not possible. I think this may be even more confusing for some people, so I've included the proof below. Theorem: If a and b are relatively prime, then a and a + b are also relatively prime. Proof: Assume a and a + b are not relatively prime (by contradiction). In this case, a = su and a + b = tu using a common divisor u ( 1). Therefore, b = tu - a = tu - su = (t - s)u. This means that a and b have a common divisor u other than 1, contradicting the statement that a and b are relatively prime. Therefore, a and a + b are relatively prime. This week's list of integers is here: https://yobinori.jp/video/integer.html Playlist is here:    • 今週の整数   ------------------------------------------------------ The "University Math and Physics" channel, where you can learn in a cram school atmosphere, mainly uploads lesson videos for: ① University Course: University-level science subjects ② High School Course: Entrance exam-level science subjects We also provide a variety of other information for high school and university science students. Crowdfunding This channel is made possible by your support. Thank you for your support! https://camp-fire.jp/projects/view/13... Official Website ▼Official Website Homepage http://yobinori.jp ▼Video List https://yobinori.jp/video.html ▼Recommended Textbooks and Reference Books https://yobinori.jp/review.html ▼Business/Collaboration Inquiries https://yobinori.jp/contact.html Member Social Media ▼Twitter Takumi (Instructor):   / yobinori   Yasu (Editor):   / yasu_yobinori   ▼Instagram Takumi (Instructor):   / yobinori   Yasu (Editor):   / yobinoriyasu   ▼note Takumi (Instructor): https://note.mu/yobinori Yasu (Editor): https://note.mu/yasu_yobinori ------------------------------------------------------ [Ending Theme] "noto" is a vocal-less music unit based on the concept of "storytelling music." This song was written as the theme song for their YouTube channel, "Learn University Math and Physics in a Prep School Style." noto / 2nd single "Telescope" (feat. Miki Natsumi) ******************************************************** The full music video is now available on the official noto YouTube channel! [noto - "Telescope"]    • noto -『Telescope』（feat.みきなつみ）   [Miki Natsumi Official YouTube Channel]    / @mikinatsu_official