112.2 問われていることとはあまり関係ないのですが nとn+1って全ての自然数において互いに素なような気が感覚的にしたのですが、例えばnとn+1が互いに素ではないときってn=何のときですか？？

480 00000 基本例題112 互いに素に関する証明問題 (1) (1) nは自然数とする。n+3は6の倍数であり,n+1は8の倍数であるとき, n+9 は 24の倍数であることを証明せよ。 (2) 任意の自然数nに対して,連続する2つの自然数nとn+1は互いに素であ ることを証明せよ。 ATUNATI p.476 基本事項 ② 基本 111 重要 114 CFS CITAT 指針 (1) 次のことを利用して証明する。 a, b, kは整数とするとき a,bは互いに素で, ak が6の倍数であるならば,hは6の倍数である。 TRAXE SHES OU MOC! (2) 1 +1は互いに素⇔nとn+1の最大公約数は nとn+1の最大公約数をg とすると n=ga, n+1=gb (a,b は互いに素) この2つの式からnを消去してg=1 を導き出す。 ポイントは 【CHART A,Bが自然数のとき, AB=1 ならば A=B=1 求める。(間 解答 (1) n+3=6k,n+1=81 (k, lは自然数)と表される。 n+9=(n+3)+6=6k+6=6(+1) n+9=(n+1)+8=81+8=8(1+1)+ M=5A JES RAJS a,bは 11 ak = bl ならばんは6の倍数, 1はαの倍数 互いに素 ②2 aとbの最大公約数は 1 <<549° よって 6(k+1)=8(+1) すなわち 3(k+1)=(2+1) 3と4は互いに素であるから,k+1は4の倍数である。このとき,l+1は3の倍数 したがって,k+1=4m (mは自然数) と表される。 である。 したがって, ゆえに n+9=6(k+1)=6.4m=24m +1=3m と表されるから, したがって, n +9 は 24の倍数である。 n+9=8.3m=24m (2) nとn+1の最大公約数をg とすると n=ga, n+1=gb (a,bは互いに素である自然数 と表される。 n = ga をn+1=gb に代入すると ga+1=gb すなわち g ( 6-α) = 1 g,a,bは自然数で,n<n+1より6-a>0であるから g g=1 (1) としてもよい。 KBT BOE-S) IS = よって, nとn+1の最大公約数は1であるから, nとn+1 (ST 8 は互いに素である。 )=(62. 注意 (2) の内容に関連した内容を,次ページの参考で扱っている。 BOSTOYEVS nは自然数とする。 n +5は7の倍数であり、 Ad>D An=ga, n+1=gb 積が1となる自然数は1だ けである。 08 S (()(A) n+7は5の倍数であるとき、

1と2答えお願いします。 早めに回答して下さるとありがたいです。

B. 本文の内容に合っているものにはTを、 間違っているものにはFをつけよう。 1. The Incas grew corn or potatoes in the terraced fields. 2. The forest around the city of Machu Picchu is not a World Heritage site. a botiziv

⑵でどうして４なのか教えて欲しいです。あと他の選択肢がダメな理由も教えてください🙏

nd OR) [A] Sports have been around for a long time. For example, an ancient wall painting shows that people enjoyed wrestling in ancient Egypt. In addition, the Olympics began in the 8th century B.C.E. in ancient Greece and many people still enjoy them today. ( A ) people have enjoyed sports for a very long time, professional sports are relatively new. This means that sports are still evolving and will continue to excite people, (B) produce many superstars. V₁ 0 V+ X Choose the appropriate word for (A) and write 1-4 on your answer sheet. 1. Since 2. Although 3. Once 4. Unless 2) Choose the appropriate words for ( B ) and write 1-4 on your answer sheet. 1. as good as 2. as long as 3. as soon as (4. as well as SENS rinolohi mela bri 3) Which of the following statements is true of the paragraph? TUI 1. Old paintings show that people enjoyed sports in ancient times. 2. The first Olympic Games were held in Italy in the 8th century B.C.E. imm 3. Professional sports have been around since the beginning of sports. ebbe liars sidi DES

全く分からないので教えてください💦

Exercises 66 2 1. Put the verb in the parentheses into its proper form. Such an easy job can (do) even by a child. 2. I think even more glass bottles should (recycle) not only in Japan but also all over the world. 3. It has begun raining hard and probably won't stop, so the game will (put off) till tomorrow. 4. A new bridge over the river must (construct) as soon as possible because of the heavy traffic both in the morning and in the evening. 5. It can safely (say) that she is telling the truth because she has no reason to tell a lie. Arrange the words in the proper order. 1. That (a boy / have / I/ known / is / since) I was a girl. 2. English (best / I/is/like / the subject). 3. Osaka is (I/ in / lived / the city / when) I was a small child. 4. Do you remember (about/I/ the story / told / what / you) I experienced during my stay in New York?

2枚目の写真の1でdがどこに書いてあるかわかりません🙏

7 英文を読んで、設問に答えなさい。 【思考・判断・表現】 (12) S Accessibility is not the norm for over 1 billion people in the world with disabilities. People with disabilities face a whole different world than the one non-disabled people live in. Thus, creating safe, comfortable, and barrier-free cities and infrastructure is urgent. Yet, accessibility for all is a matter that should draw much more attention than it is now since as we grow old, we may all need it at some point in our lives, (To enhance accessibility for wheelchair users, we can install elevators in buildings ✓高める 設 O in addition to stairways and provide adapted equipment such as screen readers for visually *impaired people to use their smartphones. AaB But, considering there are many different types of disabilities, can there be one solution to suit everybody? How can we design for all? Vi S We must remember that accessibility for all concerns and impacts all aspects of our Vt lives: whether we are shopping, commuting, using our phones, wandering in a museum, S V₁ or the streets... In sum, we must change the city organization itself. O Designers and architects need to create buildings where disabled people can get V+ S around freely and without help from other people. They will need to encounter those 移動する a who face the problems in their everyday lives to understand how to implement the 実行する solutions that are truly useful and helpful for all. The key component of *inclusive I'VE s P. あらゆる人を 2. 受け入 C 3.

空いてるとこがわからないので教えて欲しいです

SAWRY DISTRICT, 1920 Tulebug Bros. Cannery P Prestwich Primary School Miller's Lake Key: ODD Oak Avenue In apartments SAWRY DISTRICT, 2020 Yang Office Complex Lonoco Petrol Station Miller's Lake 103 houses Oak Avenue 109 shops bridge In a 109 gebly 90 10² Prestwich Primary School Elmwood River ne beach Elmwood River bike path na ina fewer people 'inconvenient ·lesh popular ·less capitaliged rural. (EN-I-1) more people 便利になった Convenient 人気になった more popular 資産が増えた more capitaliged ・都会 urban How did the city change? SOWRY DISTRICT 2 Overall, we can say that the city became more under felling 3 Much of the trees are Instead, people built Prestwich Primory School 4 Also, we can find that In 1920 to 2020, This goes across Elmwood River. renewed the beach to 5 We can also find changes about the can find it has been Petrol Station The school is now Avenue. 6 About the road, people in 1920. They changed a lot. 7 After all Sawary District changed from a convenient in 100 years. a this river, people in 1920, whereas For example, we Yang Office Complex. Also, now what is Locono (課題) along the narrow road from the Oak the branch street from Oak Avenue to go across the river. bridge which to a

高一の分詞の問題です。 （　）内の動詞を現在分詞または過去分詞に直す問題です。教えて下さい。できるだけベストアンサーにします🙇

*(1) The man stood *(2) Dave looked * (3) He kept (4) Let's go *(5) Children came *(6) He seemed (7) The treasure lies at his smartphone. (look) at the result of the game. (excite) on the bus. (talk) in the mall. (shop) to the park. (sing) to see the new building. (surprise) somewhere in the mountain. (hide)

解答お願いします。。

□03 05 04 ☐01 102 02 Of all the films released this month, the one with lots of special effects 1 is too far the most exciting. 4 <兵庫医科大> STEP 12: When it comes to learning a foreign language, nothing is more important trying to find suitable opportunities to use the language. <早稲田大 > 1 EXERCISE C >>> This air conditioner is selling the better of all the models we have in the store. (a) (b) の英文がほぼ同じ意味になるように,空所に適切な語を入れなさい。 Ja>JASX (a) Health is more important than any other thing. (b) ( ) is more important than health. < 立命館大 > (a) Elementary school students do not spend as much time playing outside as they did twenty years ago. que (dastel Vo (b) Elementary school students spend ( than they did twenty years ago. 900 ano airls telegral Common Vous ai 03 (a) Most people prefer spring to summer. (b) Most people think (h)( summer. doidw stov tirotem d ) time playing outside ) ( <日本文化大 > vindi \ vaum edt 04 (a) You have nothing to do with the incident. Nor do I. (b) I am ( ) ( ) than <日本大〉 名城大 ) involved in the incident than you are. <南山短

教えて下さると嬉しいです(><)

A. Circle the letter of the word or phrase that best completes the sentence. 1. His parents. a. intend 2. I may have to him by not allowing him to play computer games. b. locate c. motivate a. face a challenge 3. Some animals could not a. adapt 4. The building is a. based on 5. You must be a. amazing d. punish getting a job to pay for my books if the bookstore keeps raising its prices. b. come to an end d. take over c. resort to b. discover d. surround finished. They will finish working on it this month, I am sure. b. just about c. tempted to d. in touch with about your birthday next weekend. b. excited c. jealous 6. It is interesting to watch the a. energy to the colder weather, so they died. c. rank b. interaction 7. Most people imagine a desert a. empire b. factor 8. She knows how to a. repair b. reward d. medical of these two babies with each other. c. recipient almost anything that is broken. c. respond d. structure to be boring, but I find it quite interesting. c. landscape d. status d. ruin

普通にmarryとかって現在形とか過去形で使う気がするんですけど、それと何がちがうんですか？？

s 詞 + 過去分詞〉は〈be 動詞+形容詞〉であると考 英語では受動態で表される表現 be married to ~(~と結婚している) □ be crowded with ~ (~で混んでいる) be dressed in ~(~を着ている) □ be born (生まれる) □ be raised (育つ) be seated (座る) He was born and raised in Fukuoka City. (彼は生まれも育ちも福岡市だった。) ■The train was crowded with high school students. (列車は高校生でいっぱいだった。) ■Donna was dressed ir る(⇒FOCUS