Zhi-Wei Sun
Encyclopedia
Zhi-Wei Sun is a Chinese
mathematician
, working primarily on number theory
, combinatorics
, and group theory
. Currently he works as a professor in Nanjing University
.
Born in Huai'an, Jiangsu
, Sun and his twin brother Sun Zhihong proved a theorem about what are now known as the Wall-Sun-Sun prime
s that guided the search for counterexamples to Fermat's last theorem
.
In 2003, he presented a unified approach to three famous topics of Paul Erdős
in combinatorial number theory: covering systems, restricted sumsets, and zero-sum problem
s or EGZ Theorem.
He used q-series to prove that any natural number can be represented as a sum of an even square
and two triangular number
s. He conjectured, and proved with B.-K. Oh, that each positive integer can be represented as a sum of a square, an odd square and a triangular number. In 2009, he conjectured that any natural number can be written as the sum of two squares and a pentagonal number
, as the sum of a triangular number
, an even square and a pentagonal number
, and as the sum of a square, a pentagonal number
and a hexagonal number
.
He also raised many open conjectures on congruences
and posed over 100 conjectural series for powers of
.
His Erdős number
is 2. He is the Editor-in-Chief of Journal of Combinatorics and Number Theory.
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, working primarily on number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, and group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
. Currently he works as a professor in Nanjing University
Nanjing University
Nanjing University , or Nanking University, is one of the oldest and most prestigious institutions of higher learning in China...
.
Born in Huai'an, Jiangsu
Huai'an
Huai'an , known as Huaiyin before 2001, is a prefecture-level city in northern Jiangsu province of Eastern China. It borders Suqian to the northwest, Lianyungang to the north, Yancheng to the east, Yangzhou to the southeast, and the province of Anhui to the southwest.The municipality has 4,799,889...
, Sun and his twin brother Sun Zhihong proved a theorem about what are now known as the Wall-Sun-Sun prime
Wall-Sun-Sun prime
In number theory, a Wall–Sun–Sun prime or Fibonacci–Wieferich prime is a certain kind of prime number which is conjectured to exist although none are known.- Definition :...
s that guided the search for counterexamples to Fermat's last theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
.
In 2003, he presented a unified approach to three famous topics of Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
in combinatorial number theory: covering systems, restricted sumsets, and zero-sum problem
Zero-sum problem
In number theory, zero-sum problems are a certain class of combinatorial questions. In general, a finite abelian group G is considered. The zero-sum problem for the integer n is the following: Find the smallest integer k such that every sequence of elements of G with length k contains n terms that...
s or EGZ Theorem.
He used q-series to prove that any natural number can be represented as a sum of an even square
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...
and two triangular number
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
s. He conjectured, and proved with B.-K. Oh, that each positive integer can be represented as a sum of a square, an odd square and a triangular number. In 2009, he conjectured that any natural number can be written as the sum of two squares and a pentagonal number
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical...
, as the sum of a triangular number
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
, an even square and a pentagonal number
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical...
, and as the sum of a square, a pentagonal number
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical...
and a hexagonal number
Hexagonal number
A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...
.
He also raised many open conjectures on congruences
and posed over 100 conjectural series for powers of
.His Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
is 2. He is the Editor-in-Chief of Journal of Combinatorics and Number Theory.