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College of Natural Sciences (자연과학대학)
Dept. of Mathematical Sciences (수리과학부)
Theses (Master's Degree_수리과학부)

Representations by a binary quadratic form with class number 3*류수가 3인 이변수 이차형식의 표현*

- Authors
- 최재민

- Advisor
- 오병권

- Major
- 자연과학대학 수리과학부

- Issue Date
- 2013-02

- Publisher
- 서울대학교 대학원

- Description
- 학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 오병권.

- Abstract
- For integers a, b, c, the homogeneous quadratic polynomial f(x,y)=ax^2+bxy+cy^2 is called a binary quadratic form. In this thesis, we will give a closed formula on the number of integral solutions of x^2+27y^2=n for any integer n. To do this, we follow the framework given by Min and Oh, where they considered the binary form x^2+32y^2. In section 2, we briefly survey on the theory of binary quadratic forms and give some lemmas which are needed in the later. In section 3, we consider the case when n is a prime power. In section 4, we consider the case when n is any integer relatively prime to 6. In section 5, we summarize everything and give a complete formula on the number of solutions of the above equation.

- Language
- English

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