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数学 高校生

(2)の問題なのですかノートのやり方でも 合ってるのかどうかわかりません! どなたか間違ってるところがあればご指摘お願いします!

第3章 整数 問題は12ページ , |14| ユークリッドの互除法 Lv. ★★★ に素でない"は式で表しやすい。 そこで, 対偶法や背理法で示すのがポイント。 28n+5 を 21n+4 考え方 (1)条件や結論の “互いに素である" は式で表しづらいが, 否定した "互い C 21n+4 (2) (1)がヒントになっていることには気づくだろう。つまり, の形に表して,21n+4とcが互いに素であることを示せばよい。 Process 解答 対偶法で示す。 互いに 素でない2数a. bを式 a (1)aともが互いに素でないと仮定すると a= km, b=kn (kは2以上の自然数, m, nは自然数) とおくことができる。与えられた関係式に代入して kn _ _C_+d km で表す : c=k(n- md) km よって,aとcは公約数 &(2 2) をもつので, aと cは互いに素 でない。ゆえに, 対偶命題が成り立つので, もとの命題も成り (証終) 与式に代入して、 aとc が互いに素でないこと (公約数が2以上)を示 立つ。 28n+5 7n+1 す +1であるから, 28n+5と21n+4 21n+4 21n+4 が互いに素であることを証明するためには, (1)より 21n+4 と7n+1が互いに素であることを示せばよい。 21n+4 1 ここで、 +3であり, 7n+1と1は互いに 7n+1 7n+1 素であるから,(1)より 21n+4と 7n+1も互いに素である。 ゆえに,28n+5と 21n+4も互いに素である。 (証終) の解説 2つの自然数の最大公約数を求める方法をユークリッドの互除法といったが、 b +dは, ユークリッドの互除法において a, bの最大公約数を求める操作に他な a a らない。互いに素とは最大公約数が1ということであるから, 本間の背景にはユークリ ッドの互除法がある。 核心は ココ! 互いに素であることを証明するときには, 対偶法や背理法が有効 32

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英語 高校生

広島大学の二次試験対策について質問です。 去年から新しく2個の資料から問題を解く形式に変わりました。慣れるために問題を解きたいんですが、去年の分しかありません(TT) 2個の資料を用いて問題を解いていく形式の長文がある大学の過去問を知っていたら、教えて欲しいです! ↓写真... 続きを読む

(I] Read the following two passages and answer the questions. 資料1 A cave-wall depiction of a pig and buffalo hunt is the world's oldest recorded story, claim archaeologists who discovered the work on the Indonesian island Sulawesi. The scientists say the scene is more than 44,000 years old. The 4.5-metre-long panel features reddish-brown forms that seem to depict human-like figures hunting local animal species. Previously, rock paintings found in European sites dated to around 14,000 to 21,000 years old were considered to be the world's oldest clearly narrative artworks. The scientists working on the latest find say that the Indonesian art predates these. Such artworks are notoriously difficult to date because they can be made with raw materials, such as charcoal(注1), which can be much older than the paintings themselves. But scientists excited the archaeological worid when they reported, in 2014 and 2018, that caves in Sulawesi and Borneo held artworks, including animal paintings, which were older than 40,000 years. The panel seems to depict wild pigs found on Sulawesi and a species of small-bodied buffalo, called an anoa. These appear alongside smaller figures that look human but also have animal traits such as tails and long noses. In one section, an anoa is surrounded by several figures holding spears and possibly ropes. The depiction of these animal-human figures, known in mythology as therianthropes (注 2), suggests that early humans in Sulawesi had the ability to conceive of things that do not exist in the natural world, claim 2 the researchers. The oldest such example from Europe is a half-lion, half-human ivory figure from Germany that researchers have estimated to be 40,000 years old-although Some suggest that it might be significantly younger. A roughly 17,000-year-old painting of a bison chasinga bird-headed human, from Lascaux Cave in France, is considered to be one of the earliest depictions of a clear scene in European rock art. To determine the age of the hunting scene, researchers led by archaeologist Maxime Aubert, at Griffith University, Australia, analysed calcite (注 3) 'popcorn' that had built up on the painting. Radioactive uranium in the mineral slowly decays into thorium. So by measuring the relative levels of different isotopes (往0 of these elements, the researchers were able to determine that calcite on top of one pig began forming at least 43,900 years ago, and deposits (注 5) on two anoas are older than 40,900 years. The dating gives scientists clues about the origins of figurative art. "t has always been assumed that the tradition of figurative painting arose in Europe," says Alistair Pike, an archaeological scientist at the University of Southampton, UK. "This shows the tradition does not have its origins in Europe." But he notes that the researchers dated only the portions of the painting that show animals, so it's possible that the therianthropes were added later. Aubert says the team did not find calcite samples over the therianthropes. Aubert thinks the animals and the therianthropes were painted at the same time. They are of similar colour and weathered in the same way, he notes, and all the other cave art from the region is from the same time period. Archacologist Bruno David, at Monash University in Melbourne, Australia, agrees with Aubert's interpretation. If the entire painting is more than 44,000 years olid, it could mean that early humans arrived in southeast Asia with the capacity for symbolic representation and storytelling. David argues. Archaeologists have already found paint palettes and objects such as eggshells with abstract engravings made by early humans in southern Africa, he adds. “'s probably only a matter of time before narrative paintings of this, and much older age, are found in Africa." (Adapted from Nature, December 11, 2019) (注1) charcoal 木炭 (注2) therianthrope 獣人 (注3) calcite 方解石 (注4) isotope 同位体 (注5) deposit 付着物

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