127 citations · 565 across the 184 of their papers we have counts for
6 papers · 2 filters
Ten unknowns for Hilbert's tenth problem over the integers
Zhi-Wei Sun
Hilbert's Tenth Problem over the integers was solved negatively by Y. Matiyasevich in 1970. In this paper, we prove that there is no algorithm to determine for any polynomial equat…
On sums of two primes and six Fibonacci numbers
Zhi-Wei Sun
Via the circle method, we deduce that all sufficiently large positive integers are sums of two primes and six positive Fibonacci numbers, and are also sums of two primes and seven…
On Diophantine equations over the integer rings of quadratic fields
Zhi-Wei Sun
Let be any quadratic number field, and let be the ring of algebraic integers in . In 1975 J. Denef proved that Hilbert's Tenth Problem over has a negative soluti…
is diophantine over with unknowns
Zhi-Wei Sun
In 2016 J. Koenigsmann proved that is diophantine over , i.e., there is a polynomial $P(t,x_1,\ldots,x_{n})\in\mathbb Z[t,x_1,\ldots,x_{n}]…
A new kind of numbers and related congruences
Zhi-Wei Sun
For integers and , we introduce the numbers $$S_l^{(m)}(n) = \sum_{k_1,\ldots,k_l\in\mathbb N\atop k_1+\cdots+k_l = n} \binom n{k_1,\ldots,k_l}^m \ \ (n=0,1,2,\l…
On zero-sum problems of new types
Zhi-Wei Sun
In this paper, we investigate zero-sum problems of new types. For example, given integers not divisible by an integer , we prove that for some non…