全学共通科目講義(1回生〜4回生対象)
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現代の数学と数理解析 |
―― 基礎概念とその諸科学への広がり |
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日時: | 2019年5月10日(金) 16:30−18:00 |
場所: | 数理解析研究所 420号室 |
講師: | Helmke, Stefan 助教 |
題目: |
On Pell's Equation
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要約: |
Diophantine equations are polynomial equations in two or more
variables with integral coefficients such that only integral
solutions are sought. One of the simplest equations of this type
is the so-called Pell equation. Special cases of it had been
already studied in ancient Greece. The first general solution
was discovered in India around the 12th century. Independently,
an equivalent method was found by Fermat, Brouncker and Wallis
during the 17th century in Europe. The first proof that the
method always leads to all solutions of the equation is due
to Lagrange based on ideas of Euler. In this class, we will study
this interesting history of the problem, its complete solution
based on continued fractions and Lagrange's proof.
References:
(This masterfully written book contains much information about Pell's equation scattered throughout the first three chapters. In particular Sections I.IX, II.XIII and III.XII are of interest and those can also be read independently of the rest of the book.) |
"http://www.kurims.kyoto-u.ac.jp/ja/special-02.html" |