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1.x2+mx+n=0과 x2+px+q=0이 서로 같은 한 근을 가질 때 (n-p)2-(m-p)(np-mp)의 값을 구하여라. 2.993993+991991이 1984로 나누어떨어짐을 증명하여라. 3.m,n은 양의 정수 p , q는 이차방정식 4x2+mx+n=0의 서로 다른 실근, p>q일 때 방정식 x2-px+2q=0과 x2-qx+2p=0이 공통근을 가진다면 다음의 것을 구해라. (1) 공통근 (..

http://fermatslasttheorem.blogspot.com/2005/05/infinite-descent.html Infinite Descent Pierre de Fermat was very proud of his technique known as Infinite Descent. He wrote that this method "will lead to marvelous advancement in the theory of numbers" (quoted from:http://fermat.workjoke.com/flt2.htm) As he often did, Fermat left very few details on how to apply the method. He di..

http://fermatslasttheorem.blogspot.com/2005/05/fermats-last-theorem-n-3-step-4.html Fermat's Last Theorem: n = 3: Step 4 Today's blog continues the proof for Fermat's Last Theorem n=3 which was started in aprevious blog. Lemma: Given the following conditions: (a) x,y,z is a solution to x3 + y3 = z3 (b) two values of x,y,z are derived from p+q,p-q (c) p,q coprime (d) p,q opposi..

http://fermatslasttheorem.blogspot.com/2005/05/fermats-last-theorem-n-3-step-3.html Fermat's Last Theorem: n = 3: Step 3 Today's blog continues the proof for Fermat's Last Theorem n=3 that I began in a previous blog. With this step, we enter the heart of the proof for Fermat's Last Theorem n=3. This step is a bit complicated so I will only be able to provide an outline at this..

http://fermatslasttheorem.blogspot.com/2005/05/fermats-last-theorem-n-3-step-2.html Fermat's Last Theorem: n = 3: Step 2 Today's blog continues the proof that I started earlier. The full proof for Fermat's Last Theorem: n = 3 can be found in my previous blog. Today, I will show the proof for this lemma: Lemma: if p,q are coprime, p,q opposite parity, then gcd(2p,p2 + 3q2) = 1 ..

http://fermatslasttheorem.blogspot.com/2005/05/fermats-last-theorem-n-3-step-1.html Fermat's Last Theorem: n = 3: Step 1 This blog will explain the proof for the first step in Fermat's Last Theorem: n = 3. For the full proof, please start here. The details for this proof come from Leonhard Euler who was the first to make progress on Fermat's Last Theorem. The first step will b..

http://fermatslasttheorem.blogspot.com/2005/05/coprime-numbers.html CoPrime Numbers: xn + yn = znThis blog is about the equation: xn + yn = zn I will show that given any three integers that satisfy this equation, either: (a) all three of them are coprime with each other or (b) it is possible to cancel out common components and derive three numbers that are coprime. T..

http://fermatslasttheorem.blogspot.com/2005/05/fermats-last-theorem-proof-for-n3.html Fermat's Last Theorem: Proof for n=3 Leonhard Euler came up with two proofs for Fermat's Last Theorem: n = 3.One proof involved a very innovative method using irrational numbers. Unfortunately, Euler made a mistake in his proof. Despite this, his method revealed a very promising app..

안녕하세요? 책에서 보니 구면삼각형의 내각의 합은 181도에서 539까지 존재한다고 나와있던데 언뜻 그 보다 작은 값이나 큰 값의 삼각형을 그릴 수 있을 것 같기도 하고 아닌 것 같기도 하는 생각이 드는데 181도 미만이나 539도 초과의 합을 가질 수 없는 이유가 궁금합니다. 아 그..

저는 초3인데요.. 2의 200560490131제곱-1은 (메르센) 소수인가요? ----------------------------------------------------------------- 지금까지 알려진 메르센소수는 모두 47개입니다. 그중에 위에서 이야기한 소수는 들어 있지 않습니다. http://ko.wikipedia.org/wiki/%EB%A9%94%EB%A5%B4%EC%84%BC_%EC%86%8C%EC%88%98 그럼 맞..