Zhi-Wei Sun

http://maths.nju.edu.cn/~zwsun

I mainly work in the field of combinatorial number theory.

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A mysterious connection between primes and $\pi$

nt.number-theory analytic-number-theory prime-numbers sequences-and-series asked Dec 16, 2019 at 3:39

mathoverflow.net

31 votes

How to prove the identity $L(2,(\frac{\cdot}3))=\frac2{15}\sum\limits_{k=1}^\infty\frac{48^k}{k(2k-1)\binom{4k}{2k}\binom{2k}k}$?

nt.number-theory co.combinatorics analytic-number-theory sequences-and-series binomial-coefficients asked Jun 17, 2018 at 3:00

mathoverflow.net

30 votes

A conjectural trigonometric identity

co.combinatorics combinatorial-identities trigonometric-sums asked Aug 1, 2019 at 14:08

mathoverflow.net

26 votes

Can we write each positive rational number as $\frac1{p_1-1}+\ldots+\frac1{p_k-1}$ with $p_1,\ldots,p_k$ distinct primes?

nt.number-theory prime-numbers diophantine-equations unit-fractions asked Nov 29, 2018 at 9:21

mathoverflow.net

21 votes

Permutations $\pi\in S_n$ with $\sum_{k=1}^n\frac1{k+\pi(k)}=1$

nt.number-theory co.combinatorics diophantine-equations permutations asked Nov 19, 2018 at 3:08

mathoverflow.net

19 votes

A mysterious connection between primes and squares

nt.number-theory co.combinatorics prime-numbers permutations asked Nov 15, 2018 at 4:36

mathoverflow.net

18 votes

Two curious series for $1/\pi$

nt.number-theory sequences-and-series combinatorial-identities congruences ramanujan asked Aug 19, 2020 at 14:20

mathoverflow.net

18 votes

Is it true that $\{x^4+y^2+z^2:\ x,y,z\in\mathbb Z[i]\}=\{a+2bi:\ a,b\in\mathbb Z\}$?

nt.number-theory algebraic-number-theory diophantine-equations sums-of-squares asked Nov 14, 2020 at 2:43

mathoverflow.net

16 votes

The number 1680 and Lagrange's four-square theorem

nt.number-theory quadratic-forms sums-of-squares asked Jun 11, 2018 at 3:36

mathoverflow.net

15 votes

Does every integer $n>1$ have the form $a^2+b^2+3^c+5^d$ with $a,b,c,d$ nonnegative integers?

nt.number-theory diophantine-equations sums-of-squares asked May 22, 2018 at 16:22

mathoverflow.net

Top Answers

Question on a generalisation of a theorem by Euler

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Prove that $\sum_{n = 1}^{p - 1} n^{p - 1} \equiv (p - 1)! + p \pmod {p^2}$ with $p$ being an odd prime

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Gauss - Dirichlet class number formula

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Permanent identities

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Prove that there exists a nonempty subset $ I$ of $ \{1,2,...,n\}$ such that $ \sum_{i\in I}{\frac {1}{b_i}}$ is an integer

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Does $(2n)!$ divide $\det[(i^2+j^2)^n]_{0\le i,j\le n-1}$ for each integer $n>2$?

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Decide if a system of arithmetic sequences is an $m$-cover of $\mathbb{N}$

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Wanted: multiple primes in $(\frac{5n}6,n)$

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Diophantine equation for generating computably enumerable set

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Every odd integer greater than $1$ is of the form $a+b$ with $a^2+b^2$ being prime

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Can this weakening of Polignac's conjecture be proven?

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Bertrand’s Postulate apply for computer science

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Integrality of a binomial sum

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Fermat's last theorem $\pm1$

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Euler numbers and permanent of matrices

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Zhi-Wei Sun

A mysterious connection between primes and $\pi$

How to prove the identity $L(2,(\frac{\cdot}3))=\frac2{15}\sum\limits_{k=1}^\infty\frac{48^k}{k(2k-1)\binom{4k}{2k}\binom{2k}k}$?

A conjectural trigonometric identity

Can we write each positive rational number as $\frac1{p_1-1}+\ldots+\frac1{p_k-1}$ with $p_1,\ldots,p_k$ distinct primes?

Permutations $\pi\in S_n$ with $\sum_{k=1}^n\frac1{k+\pi(k)}=1$

A mysterious connection between primes and squares

Two curious series for $1/\pi$

Is it true that $\{x^4+y^2+z^2:\ x,y,z\in\mathbb Z[i]\}=\{a+2bi:\ a,b\in\mathbb Z\}$?

The number 1680 and Lagrange's four-square theorem

Does every integer $n>1$ have the form $a^2+b^2+3^c+5^d$ with $a,b,c,d$ nonnegative integers?