(in Japanese)

About me

I was a Global COE PD at Department of Mathematics at Kyoto University.

2000, Faculty of Science, Kyoto University
2004, Department of Mathematics at Kyoto University
2009/4-2013/3, GCOE-PD at Department of Mathematics at Kyoto University
2010/10-2012/3, Part-time teacher at Kyoto University(Additional)
2012/8- Part-time teacher at CJLC of Osaka University(Additional)
2013/4-, Part-time teacher at Kyoto Kyoiku University(Additional)
2020/4-, Part-time teacher at Kobe University(Additional)

e-mail: y64k at chive.ocn.ne.jp (at should be replaced by @) (4/28/2021) I cannot receive e-mails to this e-mail address until 5/7/2021.

twitter: https://twitter.com/tyamada1093

My Interests

I am interested in easily stated problems in number theory and discrete mathematics. Many of such problems are formulated and discussed by elementary number theory, analytic number theory, combinatorics, graph theory, computability theory and others.

• Primes of special form, such as prime k-tuple
  
• The abc conjecture
  
• Numbers with special property involving divisors, such as perfect numbers
  
• Residual orders and Discrete logarithms modulo a prime or a prime power
  
• Integer sequences with special additive property, such as Sidon sets
  
• Combinatorial Design
  
• Ramsey Theory
  
• Cardinals
  
• Computational property of number theoretic algorithms and combinatorial algorithms
  

At present, my research interest lies in properties of values of classical arithmetic functions related to divisors of integers, such as σ and φ.

Courses (2023)

Kobe Univ. / Calculus B1, B2 (Apr.-Aug. / Tue / 8:50-10:20)

(5/30) Digest / 1Q, 7th (Japanese) tex pdf

(5/23) Digest / 1Q, 6th (Japanese) tex pdf Supplement on 5th and 6th classes (Japanese) tex pdf

(5/9) Digest / 1Q, 4th (Japanese) tex pdf Report problems tex pdf

(4/18) Digest / 1Q, 2nd (Japanese) tex pdf

(4/11) Digest / 1Q, 1st (Japanese) tex pdf Supplement on completeness of real numbers (Japanese) tex pdf

Courses (2022)

Kobe Univ. / Calculus A1, A2 (Apr.-Aug. / Tue / 10:40-12:10)

(6/7) Exam problems / 1Q, 7th (in Japanese) tex pdf Answers (in Japanese) tex pdf

(5/21) Report problems / 1Q, 5th (in Japanese) tex pdf

Kobe Univ. / Calculus B1, B2 (Apr.-Aug. / Tue / 8:50-10:20)

(6/7) Exam problems / 1Q, 7th (in Japanese) tex pdf Answers (in Japanese) tex pdf

(5/21) Report problems / 1Q, 5th (in Japanese) tex pdf

(5/21) Addendum / 1Q, 2th (in Japanese) tex pdf

Courses (2020)

Kobe Univ. / Calculus B3, B4 (Oct.-Feb. / Tue / 10:40-12:10)

(2/2) Digest and Exercises / 3Q, 8th (in Japanese) tex pdf

(1/26) Digest and Exercises / 3Q, 7th (in Japanese) tex pdf Answers to exercises in 7th (in Japanese) tex pdf

(1/19) Digest and Exercises / 3Q, 6th (in Japanese) tex pdf Answers to exercises in 6th (in Japanese) tex pdf Supplement (in Japanese) tex pdf

(1/12) Digest and Exercises / 3Q, 5th (in Japanese) tex pdf Answers to exercises in 4th-5th (in Japanese) tex pdf

(12/22) Digest and Exercises / 3Q, 4th (in Japanese) tex pdf, revised ver. tex pdf Supplement (in Japanese) zip (source) pdf

(12/15) Digest and Exercises / 3Q, 3rd (in Japanese) tex pdf Answers to exercises in 3th (in Japanese) tex pdf

(12/8) Digest and Exercises / 3Q, 2nd (in Japanese) tex pdf Answers to exercises in 2nd (in Japanese) tex pdf

(12/1) Digest and Exercises / 3Q, 1st (in Japanese) tex pdf Supplement (in Japanese) tex pdf Answers to exercises in 1st (in Japanese) tex pdf

(11/19) Digest and Exercises / 3Q, 7th (in Japanese) tex pdf Answers to exercises in 7th (in Japanese) tex pdf

(11/12) Digest and Exercises / 3Q, 6th (in Japanese) tex pdf Answers to exercises in 6th (in Japanese) tex pdf

(11/10) Digest and Exercises / 3Q, 5th (in Japanese) tex pdf Answers to exercises in 5th (in Japanese) tex pdf

(10/27) Digest and Exercises / 3Q, 4th (in Japanese) tex pdf Answers to exercises in 3rd-4th (in Japanese) tex pdf

(10/20) Digest and Exercises / 3Q, 3rd (in Japanese) tex pdf

(10/13) Digest and Exercises / 3Q, 2nd (in Japanese) tex pdf Answers to exercises in 1st-2nd (in Japanese) tex pdf

(10/6) Digest and Exercises / 3Q, 1st (in Japanese) tex pdf

Kobe Univ. / Calculus A1, A2 (Apr.-Aug. / Tue / 10:55-12:40)

(8/11) Digest and Exercises / 2Q, 7th (in Japanese) tex pdf

(8/4) Digest and Exercises / 2Q, 6th (in Japanese) tex pdf

(7/28) Digest and Exercises / 2Q, 5th (in Japanese) tex pdf

(7/21) Digest and Exercises / 2Q, 4th (in Japanese) tex pdf

(7/14) Digest and Exercises / 2Q, 3rd (in Japanese) tex pdf

(7/7) Digest and Exercises / 2Q, 2nd (in Japanese) tex pdf

(6/30) Digest and Exercises / 2Q, 1st (in Japanese) tex pdf

(6/23) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf (7/20/2020 added) Answers to the 7th exercises tex pdf

(6/16) Digest and Exercises / 1Q, 6th (in Japanese) tex pdf

(6/9) Digest and Exercises / 1Q, 5th (in Japanese) tex pdf

(6/2) Digest and Exercises / 1Q, 4th (in Japanese) tex pdf

(5/27) Digest and Exercises / 1Q, 3rd (in Japanese) tex pdf

(5/20) Digest and Exercises / 1Q, 2nd (in Japanese) tex pdf

(5/13) Digest and Exercises / 1Q, 1st (in Japanese) tex pdf

Kobe Univ. / Calculus B1, B2 (Apr.-Aug. / Tue / 8:50-10:35)

(8/11) Digest and Exercises / 2Q, 7th (in Japanese) tex pdf

(8/4) Digest and Exercises / 2Q, 6th (in Japanese) tex pdf

(7/28) Digest and Exercises / 2Q, 5th (in Japanese) tex pdf

(7/21) Digest and Exercises / 2Q, 4th (in Japanese) tex pdf

(7/14) Digest and Exercises / 2Q, 3rd (in Japanese) tex pdf

(7/7) Digest and Exercises / 2Q, 2nd (in Japanese) tex pdf

(6/30) Digest and Exercises / 2Q, 1st (in Japanese) tex pdf

(6/23) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf (7/18/2020 added) Answers to the 7th exercises tex pdf

(6/16) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf

(6/9) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf

(6/2) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf

(5/27) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf

(5/20) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf

(5/13) Digest and Exercises / 1Q, 7th (in Japanese) tex pdf

Courses (2017)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/25) Report Problems tex (in Japanese) pdf (in Japanese)

• (2018/2/18 added) Sketch of answers tex pdf

(6/17) Report Problems tex (in Japanese) pdf (in Japanese)

• (2018/2/18 added) Sketch of answers tex pdf

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(8/1) Extra exercises tex (in Japanese) pdf (in Japanese) (8/4 revised) tex (in Japanese) pdf (in Japanese) Figures (zip)

Courses (2016)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/28) Term-End Report Problems tex (in Japanese) pdf (in Japanese)

• (2018/2/18 added) Sketch of answers tex pdf

(6/17) Report Problems tex (in Japanese) pdf (in Japanese)

• (2018/2/18 added) Sketch of answers tex pdf

Courses (2015)

Kyoto Kyoiku Univ. / Linear Algebra II (Apr.-Jul. / Fri / 12:50-14:20)

(7/28) Linear mappings between vector spaces tex (in Japanese) pdf (in Japanese)

(7/17) Term-End Report Problems tex (in Japanese) pdf (in Japanese)

(7/17) Sums and intersections of vector spaces tex (in Japanese) pdf (in Japanese)

(6/30) Vector spaces tex (in Japanese) pdf (in Japanese) (Addendum) tex (in Japanese) pdf (in Japanese)

(6/6) Report Problems tex (in Japanese) pdf (in Japanese)

(6/5) Linear transformations in plane and space tex (in Japanese) pdf (in Japanese)

(5/29) Vectors in plane and space tex (in Japanese) pdf (in Japanese)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(8/20) Outline of answers of the examination problems tex (in Japanese) pdf (in Japanese)

Courses (2014)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Oct.-Feb. / Fri / 12:50-14:20)

(1/18) Calculation of fractions tex (in Japanese) pdf (in Japanese)

See old lecture notes for calculation of natural numbers.

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(7/29) The 5-6th lectures tex (in Japanese) pdf (in Japanese)

(7/29) The 4-5th lectures tex (in Japanese) pdf (in Japanese)

(7/22) The third-4th lectures tex (in Japanese) pdf (in Japanese)

(5/27) The second-third lectures tex (in Japanese) pdf (in Japanese)

• Set theoretical definition of addition of natural numbers, the associative law and the commutative law involving multi-terms and a problem concerning to palindromic numbers are added

(5/13) The first-second lectures tex (Unicode, in Japanese) pdf (in Japanese)

• Set theoretical definition of natural numbers is added

Courses (2013)

Kyoto Kyoiku Univ. / The subject "arithmetic" in elementary school (Apr.-Jul. / Tue / 12:50-14:20)

(5/7) The first lecture tex (Unicode, in Japanese) pdf (in Japanese)

(5/20) The second-third lecture tex (in Japanese) pdf

Courses (2011)

Kyoto Univ. / Basic Mathematics IA (Fri / 8:45-10:15, 10:30-12:00)

The examination was held in July 29. It mainly concerns to convergence and limit of sequences and differentiation of functions.

• Problems in the examination held in July 29, 8:45-10:15(in Japanese)
• Problems in the examination held in July 29, 10:30-12:00(in Japanese)

Here is the homework given in Jul 8, Deadline Apr 5. It concerns to differentiation, integration and convergence of series. It is not obligatory.

• Homework in Jul 8 (in Japanese)

Here is the homework given in May 20, Deadline July 1. It mainly concerns to convergence of real sequences. It is not obligatory.

• Homework in May 20 (in Japanese)
• On the supremum of a set (related to homework in May 20) (7/6)
• Solutions of homework in May 20 (7/6)

Course (2010)

Kyoto Univ. / Linear Algebra B (Wed / 10:30-12:00)

The examination was held in January 26. It mainly concerns to linear mappings between vector spaces, the method of least squares and the eigenvalue problem.

• Problems and solutions of the quiz held in January 26 (in Japanese)

A quiz was held in December 8. It mainly concerns to linear independence of vectors.

• Problems and solutions of the quiz held in December 8 (in Japanese)

Documents

Proofs of the infinitude of primes (dvi)(1/12/2010, 8/7/2014, 11/12/2018 revised) (pdf) (8/7/2014 pdf updated TeX source(1/12/2010, 8/7/2014, 11/12/2018 revised)

Proofs of the fundamental theorem of arithmetic (dvi) (7/1/2015)(6/4/2019 revised) Proofs of the fundamental theorem of arithmetic (pdf) (7/1/2015)(6/4/2019 revised) TeX source (7/1/2015)(6/4/2019 revised)

Publications

1. Odd perfect numbers of a special form, Colloq. Math. 103 (2005), 303--307. dvi tex
2. Unitary super perfect numbers, Math. Pannon. 19 (2008), 37--47. dvi tex
3. Linear equations involving iterates of $\sigma(N)$, INTEGERS 9 supplement A15. dvi tex
4. On diophantine equations $x^m=y^{n_1}+y^{n_2}+\ldots +y^{n_k}$, Glasgow Math. J. 51 (2009), 143--148. dvi tex
5. On the simoultaneous equations $\sigma(2^a)=p^{f_1}q^{g_1}, \sigma(3^b)=p^{f_2}q^{g_2}, \sigma(5^c)=p^{f_3}q^{g_3}$, Publ. Math. Debrecen 93 (2018), 57--71, the preprint version in arXiv.
   • (2017/4/6, 2018/11/11 added) The digest version has been published in RIMS Kôkyûroku, 1874 (2014), 215--223 as Proceedings' paper of the workshop Analytic Number Theory -- Number Theory through Approximation and Asymptotics. This version contains some errors, which are revised in the PMD version.
6. Infinitary superperfect numbers Ann. Math. Inform. 47 (2017), 211--218, see the journal's website.
7. On equations $\sigma(n)=\sigma(n+k)$ and $\varphi(n)=\varphi(n+k)$, J. Combin. Number Theory 9 (2017), 15--21, the author's final version in arXiv.
8. 2 and 9 are the only biunitary superperfect numbers, Ann. Univ. Sci. Budapest. Sect. Comput. 48 (2018), 247--256, see the journal's website.
9. A new upper bound for odd perfect numbers of a special form, Colloq. Math. 156 (2019), 15--23.
10. Quasiperfect numbers with the same exponent, INTEGERS 19 (2019), A35.
11. A generalization of the Ramanujan-Nagell equation, Glasgow Math. J. 61 (2019), 535--544.
12. (6/29/2020) Revisions to our preprint "Three-term Machin-type Formulae", arxiv:1811.09273, txt.
13. An analog of perfect numbers involving the unitary totient function, J. Number Theory. 209 (2020), 246--266, the author's final version in arXiv.
14. On Sinha's note on perfect numbers, Ann. Univ. Sci. Budapest. Sect. Comput. 51 (2020), 301--308, see the journal's website.
15. On finiteness of odd superperfect numbers, J. Th. Nombres Bordeaux 32 (2020), 259--274.
16. On the divisibility of odd perfect numbers, quasiperfect numbers and amicable numbers by a high power of a prime, INTEGERS 20 (2020), A91.
17. Almost Lehmer Numbers, J. Integer Seq. 24 (2021), Article 21.5.5.

Talks

An exponential diophantine equation related to odd perfect numbers (at Diophantine Analysis and Related Fields 2018) pdf (3/4/2018) source (3/4/2018)

Three-term Machin-type formulae (at RIMS Workshop 2018 "Analytic Number Theory and Related Topics" , 10/29/2018) (11/12/2018) (pdf) source (zip) (6/29/2020 added) See also the above preprint and revision list.

Almost Lehmer numbers (at RIMS Workshop 2020 "Problems and Prospects in Analytic Number Theory" , 11/27/2020) (12/7/2020, with revision) (pdf) source (zip) (4/28/2021 added) See also the above paper.

Links

arXiv.org

Number Theory Web

Number Theory List

The Mathematical Society of Japan

(2017/4/6 added)The On-Line Encyclopedia of Integer Sequences (OEIS)