Mathematical Lectures or Talks

Simple Ideas for Famous Problems, 1996. Various Number-theoretic Quotients and Related Congruences, 2000. Recent Progress on Covers of the Integers and Their Applications, 2000. On Hilbert's Tenth Problem and Related Topics, 2000. Recent Progress on Combinatorial Number Theory (Chinese), 2001. Equalities and Inequalities Related to Covers of Z or Groups, 2002. On the Structure of Periodic Arithmetical Maps, 2002. New Results on Subset Sums, 2002. On Zero-sum Problems, 2002. On the Sum $\sum_{k\equiv r (mod m)}\binom nk$ and Related Results, 2002. Introduction to Bernoulli and Euler Polynomials, 2002. Problems and Results in Combinatorial Number Theory, 2002. Sumsets with Polynomial Restrictions, 2002. The Magic of Mathematics (Chinese), 2002, 2006. How to Unify Covering Systems, Restricted Sumsets and Zero-sum Problems, 2003. Recent Progress on Zero-sum Problems and Snevily's Conjecture, 2004. Covering Systems and their Connections to Zero-sums, 2004. On Disjoint Systems of Residue Classes or Cosets of Subgroups, 2004. On Various Combinatorial Sums and Related Identities, 2004. Two Local-Global Theorems and a Powerful Formula, 2004. Groups and Combinatorial Number Theory, 2004. On Some Conjectures of Erdos-Heilbronn, Lev and Snevily, 2004, 2005. Problems and Results on Covering Systems, 2005. Some Congruences Motivated by Algebraic Topology, 2005. Some Curious Results on Bernoulli and Euler Polynomials, 2005, 2006. A Survey of Zero-sum Problems on Abelian Groups, 2006. Recent Progress on Congruences involving Binomial Coefficients, 2006. Covering Systems and Periodic Arithmetical Functions, 2006. Combinatorial Aspects of Covers of Groups by Cosets or Subgroups, 2006. Curious Identities and Congruences involving Bernoulli Polynomials, 2006. Combinatorial Aspects of Szemeredi's Theorem, 2007. Additive Combinatorics and Latin Transversals, 2007. Sums of Squares and Triangular Numbers, and Rado Numbers for Linear Equations, 2007. An Additive Theorem Related to Latin Transversals, 2007. Some Famous Problems and Related Results in Combinatorial Number Theory, 2007. Groups in Combinatorial Number Theory, 2007. Various Extensions of Some Basic Results in Combinatorial Number Theory, 2008. Recent Problems and Results Involving Binomial Coefficients, 2008. An Extremal Problem on Covers of Abelian Groups, 2008. Study Covers of Groups via Characters and Number Theory, 2008. On Representations of Integers Involving Triangular Numbers, 2008. Some New Conjectures Involving Primes, 2009. Problems and Results in Additive Combinatorics, 2009. Polygonal Numbers, Primes and Ternary Quadratic Forms, 2009. Combinatorial Number Theory in China, 2009. On the DKSS Technique and the DKSS Conjecture, 2010. Some Sophisticated Applications of the Combinatorial Nullstellensatz, 2010. Conjectures and Results on Super Congruences, 2010. Conjectures for Super Congruences and Series for π and Other Constants (45 minutes version), 2010. Conjectures for Super Congruences and Series for π and Other Constants (30 minutes version), 2010. Super Congruences involving Binomial Coefficients and New Series for some Famous Constants, 2010. Arithmetic Properties of Combinatorial Quantities, 2010. On Divisibility concerning Binomial Coefficients, 2010. Correspondence between Series and Congruences, 2010. On Weighted Extension of the Erdos-Heilbronn Conjecture, 2011. On the DKSS Conjecture for Finite Abelian Groups, 2011. Number Theory behind Series for Powers of π, 2011. Conjectures and Results on x2 mod p2 with 4p=x2+dy2, 2011. Combinatorial Congruences via the Zeilberger Algorithm, 2011. On Arithmetic Properties of Bell Numbers, Delannoy Numbers and Schroder Numbers, 2011. Conjectures and Results on Generalized Trinomial Coefficients and Motzkin Numbers, 2011. Some Sophisticated Congruences involving Fibonacci Numbers, 2011. Some of my Number-theoretic Conjectures and related Progress, 2011. Historical Remarks on my Conjectural Congruences and Series for 1/π, 2011. Primes from the Viewpoint of Combinatorics, 2012. p-adic Congruences Motivated by Series, 2012. Various New Observations about Primes, 2012. Conjectures involving Arithmetical Sequences, 2012. The Riddle of Primes, 2012. Apery Numbers, Franel Numbers and Binary Quadratic Forms, 2013. Some New Representation Problems involving Primes, 2013. Combinatorial Congruences via Zeilberger's Algorithm and Trees with Prime Vertices, 2013. Some Open Combinatorial Congruences, 2013. Write n = k + m with f(k,m) Prime, 2013. Congruences for Franel Numbers, 2014. Problems on Combinatorial Properties of Primes, 2014. On Some Arithmetic Functions, 2014. Towards the Twin Prime Conjecture, 2014. Supercongruences Motivated by e, 2014. On Generalized Central Trinomial Coefficients, 2015. On Universal Sums involving Polygonal Numbers, 2015. New Divisibility Results on Certain Sums of Binomial Coefficients, 2015. On g_n(x)=sum_{k=0}^n binom(n,k)^2*binom(2k,k)*x^k and Related Topics, 2015. On Primes in Arithmetic Progressions, 2015. Some New Problems and Results in Combinatorial and Additive Number Theory, 2016. Some New Diophantine Problems, 2016. A New Result in Combinatorial Number Theory, 2016. Combinatorial Quantities and Arithmetic Means, 2016. Refining Lagrange's Four-square Theorem, 2016. The 1-3-5-Conjecture and Related Topics, 2016-2017. The Three-Square Theorem and its Application, 2017. Restricted Sums of Three or Four Squares, 2017. Further Results on Hilbert's Tenth Problem, 2017. On Hilbert's Tenth Problem, 2017. A Survey of Arithmetic Properties of Combinatorial Quantities, 2017. On Snevily's Conjecture and Related Topics, 2017. Introduction to Lucas Sequences, 2017. On Universal Sums x(ax+b)/2+y(cy+d)/2+z(ez+f)/2, 2017. On Covers of Groups by Cosets, 2018. Problems and Results on Sums of Squares, 2018. Determinants, Permutations and Additive Combinatorics, 2018. Historical Remarks on my Conjectural Series, 2018-2019. On Permutations and Identities related to Quadratic Residues, 2018. On Some Determinants involving Legendre or Jacobi Symbols, 2018-2019. Problems and Results on Permutations, 2019. Riddles of Representations of Integers, 2019. Computability and Undecidability, 2019. Trigonometric Identities and Quadratic Residues, 2019. Proof of Some Conjectures involving Quadratic Residues, 2020. A Lecture on Cantor's Set Theory (in Chinese), 2020. A Lecture on Russell's Paradox and the Third Mathematical Crisis (in Chinese), 2020. New Series for Powers of π and Their q-Analogues, 2020. Introduction to Combinatorial Number Theory (I) -- Bernoulli Numbers and Euler Numbers, 2020 Introduction to Combinatorial Number Theory (II) -- Combinatorial Congruences, 2020 Introduction to Combinatorial Number Theory (III) -- π-Series and Their p-adic Analogues, 2020 Introduction to Combinatorial Number Theory (IV) -- Sumsets and Zero-sum Problems, 2020 Introduction to Combinatorial Number Theory (V) -- Combinatorial Nullstellensatz and its Applications, 2020 Introduction to Combinatorial Number Theory (VI) -- Permutations, Determinants and Permutations, 2020 Two Local-Global Theorems related to Covers of the Integers, 2020 Zero-sum Problems for Abelian Groups and Covers of the Integers by Residue Classes, 2020 On Restricted Sumsets, 2020 On Two Products modulo Primes, 2020 Various Refinements of Lagrange's Four-Square Theorem, 2020 Seeking for π-series in August 2020, 2020 Hamilton Quaternions and the 1-3-5 Conjecture, 2020 Combinatorial Ideas related to Hilbert's Tenth Problem, 2020 Riddles of Representations of Integers, 2020 Covers of the Integers by Residue Classes and their Extensions to Groups, 2021. The 11 Unknowns Theorem and its Applications, 2021. Hilbert's Tenth Problem and its Further Developments, 2021. Behind Mathematical Discoveries, 2022. New Results on Power Residues modulo Primes, 2022. Mysterious π-Series (I), 2022. Mysterious π-Series (II), 2023. Series and Congruences involving Harmonic Numbers, 2023. A Survey of Series for 1/π Conjectured by Me, 2023. Progress on Questions in the book "New Conjectures in Number Theory and Combinatorics", 2024.

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