Thanks to Martin Gardner
1) Prove that a^n - b^n is divisible by (a-b)
( you can juggle your way through this one without too much difficulty. For n being even, you split it as you know how so you only have to prove it for the case of n being odd. https://math.stackexchange.com/questions/188657/why-is-an-bn-divisible-by-a-b)
2) Prove that 10^(2k+1) + 1 (i.e., 11, 1001, 100001, etc) is divisible by 11 and that 10^2k - 1 (i.e., 99, 9999, etc) is divisible by 11
3) Prove that a palindromic prime number must have an odd number of digits.
Thanks of course to Martin Gardner :)
Butter by Asako Yuzuki: A Spoiler-Free Cast of Characters
Butter, by Asako Yuzuki, introduces a fairly large cast of journalists, friends, relatives, and people connected with the criminal case at the center of the novel. If you're partway through the book and find yourself asking, “Wait — who was that again?”, this spoiler-free guide should help.
The characters below are arranged primarily by their relationship to Rika Machida, the journalist at the center of the story, and Manako Kajii, the imprisoned woman Rika sets out to interview.
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| Character | Connection | Who They Are |
|---|---|---|
| Rika Machida | Central character | A 33-year-old journalist at Shūmei Weekly. She becomes interested in interviewing Manako Kajii and investigating the sensational case surrounding her. |
| Manako Kajii | Rika's interview subject | The imprisoned woman at the center of the novel. Kajii is an accomplished cook and passionate food lover who has been convicted in connection with the deaths of men she met through dating sites. The press sometimes refers to her as Kajimana. |
| Reiko Sayama | Rika's best friend | Rika's close friend since university. She has stepped away from her career and is concentrating on married life and trying to have a child. She is one of the novel's most important characters. |
| Ryōsuke Sayama | Reiko's husband | Reiko's husband, who works for a confectionery company. An easy memory aid: Reiko = Rika's friend; Ryōsuke = Reiko's husband. |
| Makoto Fujimura | Rika's boyfriend | An editor in the books division of the same publishing company where Rika works. Their relationship is fairly casual at the beginning of the novel. |
| Yoshinori Shinoi | Rika's professional contact | An older and more experienced journalist and editor who serves as a useful professional contact for Rika and provides her with information and leads. |
| Kitamura | Rika's coworker | A younger male reporter at Shūmei Weekly who works alongside Rika. |
| Yū Uchimura | Rika's junior colleague | A younger woman at Rika's publishing company who is friendly and enthusiastic toward her. |
| Misaki Machida | Rika's mother | Rika's mother, who raised her largely on her own after separating from Rika's father. |
| Masako | Kajii's mother | The mother of Manako Kajii and Anna, associated with Kajii's family background in Niigata. |
| Anna | Kajii's younger sister | Manako Kajii's younger sister. Through her, the reader gets another connection to Kajii's family and earlier life. |
| Tokio Yamamura | Connected to the Kajii case | One of the men whose death is associated with the criminal case surrounding Kajii. |
| Hatoko Yamamura | Tokio's sister | A relative of one of the men involved in the Kajii case. Rika encounters her through her reporting. |
| Shirō Yokota | Connected to Kajii's past | A man who knew Kajii before her arrest. Knowing simply that he belongs to Kajii's earlier life is enough when his name first appears. |
| Miyuko Sasazuka (“Madame”) | Cooking-school figure | The woman who runs Le Salon de Miyuko, a cooking school connected with Kajii. |
| Chizu | Cooking-school figure | A student at Le Salon de Miyuko who knew Kajii through the school. |
| Taiichi Akiyama | Connected to Kajii's hometown | A dairy farmer from the area where Kajii grew up. |
| Mizushima | Rika's work world | A former colleague of Rika's who moved to the books department. |
| Saya Kamiyama | Shinoi's family | Shinoi's daughter. For purposes of keeping the names straight, remembering Saya = Shinoi's daughter is enough. |
The Relationships Worth Remembering
You don't need to memorize everybody. Most of the early name confusion disappears if you keep these six relationships straight:
- Rika ↔ Kajii: journalist and interview subject
- Rika ↔ Reiko: best friends
- Reiko ↔ Ryōsuke: wife and husband
- Rika ↔ Makoto: dating
- Rika ↔ Shinoi: journalist and older professional contact
- Kajii ↔ Masako and Anna: mother and younger sister
Above all, keep Rika, Kajii, and Reiko firmly in mind. They form the central human triangle around which much of the novel develops. The other names become much easier to place once those three are familiar.
This guide deliberately avoids explaining later developments in the plot, so it can be used as a reference while reading without spoiling the novel.