个人简历

主要课程
离散数学、近世代数、基础数论、组合数学
Research Interests
　　　 Number Theory (especially Combinatorial Number Theory),
　　　 Combinatorics, Group Theory, Mathematical Logic.
Academic Service
　　　 Editor-in-Chief of Journal of Combinatorics and Number Theory, 2009--.
　　　　 You may submit your paper by sending the pdf file to zwsun@nju.edu.cn
　　　　 or to one of the two managing editors Florian Luca and Jiang Zeng. (A sample tex file)
　　　 Editorial Board Member of Electronic Research Archive, 2019--.
　　　 Reviewer for Zentralblatt Math., 2007--.
　　　 Reviewer for Mathematical Reviews, 1992--.
　　　 Referee for Adv. in Math., Proc. Amer. Math. Soc., Acta Arith., J. Number Theory, J. Combin. Theory Ser. A, European J. Combin.,
　　　　 Finite Fields Appl., Adv. in Appl. Math., Discrete Math., Discrete Appl. Math., Ramanujan J., SIAM Review etc.
　　　 I refuse to referee papers for any open access journal which asks for page charges.
School Education and Employment History
　　　1980.9--1983.7 The High Middle School Attached to Nanjing Normal Univ.
　　　1983.9--1992.6 Department of Mathematics, Nanjing University (Undergraduate--Ph. D. Candidate; B. Sc. 1987, Ph. D. 1992)
　　　1992.7-- 　　　 Teacher in Department of Mathematics, Nanjing University
　　　1994.4--1998.3 Associate Professor in Math.
　　　1998.4-- 　　　 Full Professor in Math.
　　　1999.11- 　　　 Supervisor of Ph. D. students
My paper Further results on Hilbert's Tenth Problem (based on my PhD thesis in 1992)
My book New Conjectures in Number Theory and Combinatorics (which collects 820 open conjectures posed by me)
My Favorite Conjecture with $3500 (3500 US dollars) Prize for the First Proof (see OEIS A303389, A303540 and A303821 for similar conjectures)Any integer n > 1 can be written as a2 + b2 + 3c + 5d with a, b, c, d nonnegative integers. [This has been verified for n up to 2*1010.]
My Four-square Conjecture with $2500 Prize for the First Proof Every n = 2,3,... can be written as x2 + y2 + (2a3b)2 + (2c5d)2, where x,y,a,b,c,d are nonnegative integers. [This has been verified for n up to 1010 by Giovanni Resta.]
My 2-4-6-8 Conjecture with $2468 Prize for the First Proof Any positive integer n can be written as binom(w,2) + binom(x,4) + binom(y,6) + binom(z,8) with w,x,y,z integers greater than one. [This has been verified for n up to 2*1012 by Yaakov Baruch.]
My 24-Conjecture with $2400 Prize (see also OEIS A281976 and arXiv:1701.05868）Any natural number n can be written as the sum of squares of four nonnegative integers x, y, z and w such that both x and x+24y are squares. [This has been verified for n up to 1010 by Qing-Hu Hou.]
My Conjecture involving Primes and Powers of 2 with $1000 Prize (see also Conjecture 3.6(i) of this paper) Every n = 2, 3, ... can be written as a sum of two positive integers k and m such that 2k + m is prime. [This has been verified for n up to 107.]
My Conjecture on Alternating Sums of Consecutive Primes with $1000 Prize (see Conj. 1.3 of this published paper) For any positive integer m, there are consecutive primes pk,...,pn (k < n) not exceeding 2m+2.2*sqrt(m) such that m = pn - pn-1 + ... + (-1)n-k pk, where pj denotes the j-th prime. [This has been verified for m up to 109 by Chang Zhang.]
My Conjecture on Unit Fractions involving Primes with $500 Prize (see also Conjecture 4.1(i)-(ii) of this paper) Let d be -1 or 1. Each positive rational number can be written as 1/(p(1)+d) + 1/(p(2)+d) + ... + 1/(p(k)+d), where p(1),...,p(k) are distinct primes.
My Conjecture on Primitive Roots of the Form x2+1 with 2000 RMB Prize (see OEIS A239957, A241476 and Conj. 3.1 of this paper) For any prime p, there is an integer 0 < g < p with g-1 an integer square such that g is a primitive root modulo p. [I verified this for all primes below 107. Later, C. Greathouse extended the verification to all primes below 1010.]
My 1680-Conjecture with 1680 RMB Prize (see also OEIS A280831 and Conjecture 4.10(iv) of this published paper） Any natural number n can be written as the sum of squares of four nonnegative integers x, y, z and w such that x4 + 1680y3z is a square. [This has been verified for n up to 108 by Qing-Hu Hou.]
My Conjecture on the Representation n = x4 + y3 + z2 + 2k with $234 Prize (see also Conjecture 6.1(i) of this paper)Each n = 2,3,... can be written as x4 + y3 + z2 + 2k with x,y,z nonnegative integers and k a positive integer. [This has been verified by Qing-Hu Hou for n up to 109.]
My Conjecture on Primes of the Form x2+ny2 with $200 Prize (see also Conjecture 2.21(i) of this paper)Each n = 2,3,... can be written as x+y with x and y positive integers such that x+ny and x2+ny2 are both prime.
My Little 1-3-5 Conjecture with $135 Prize (see this paper for more such conjectures) Each n = 0,1,2,... can be written as x(x+1)/2+y(3y+1)/2+z(5z+1)/2 with x,y,z nonnegative integers. [I have proved the weaker version with x,y,z integers.]
My Conjecture related to Bertrand's Postulate with $100 Prize (see also Conjecture 2.18 of this paper)Let n be any positive integer. Then, for some k=0,...n, both n+k and n+k2 are prime. [I have verified this conjecture for n up to 200,000,000.]
My 100 Conjectures on Representations involving Primes or related Things
My 60 Open Problems on Combinatorial Properties of Primes
My Conjecture on the Prime-Counting Function (see Conjectures 2.1, 2.6 and 2.22 of this paper)
　(i) For any integer n>1, π(k*n) is prime for some k = 1,...,n, where π(x) denotes the number of primes not exceeding x. [I have verified this for n up to 107. See OEIS A237578.]
　(ii) For every positive integer n, π(π(k*n)) is a square for some k = 1,...,n. [I have verified this for n up to 2*105. See OEIS A238902 and OEIS A239884.]
　(iii) For each integer n>2, π(n-p) is a square for some prime p < n. [I have verified this for n up to 5*108. See OEIS A237706 and OEIS A237710.]
My \

研究领域

"数论（特别是组合数论）与组合数学"