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most citedTrigonometric Parallaxes of Massive Star Forming Regions: VI. Galactic Structure, Fundamental Parameters and Non-Circular Motions

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4 papers · 2 filters

math.NT2009

Some q-congruences related to 3-adic valuations

Hao Pan, Zhi-Wei Sun

In 1992 Strauss, Shallit and Zagier proved that for any positive integer $a$ we have $k = 0 \sum 3^{a} - 1 (k 2 k) = 0 (m o d 3^{2 a})$ and furthermore $$3^{-2a}}\sum_{k=0}^{3^a-1}…

math.NT2009

On the number of distinct prime factors of $nj + a^{h} k$

Hao Pan

Let $ω (n)$ denote the number of distinct prime factors of $n$ . Then for any given $K \geq 2$ , small $ε > 0$ and sufficiently large (only depending on $K$ and $ε$ ) $x$ , there exist at…

math.NT2009★ 1 cited

On the integers not of the form $p + 2^{a} + 2^{b}$

Hao Pan

We prove that |{1<=y<=x: y is odd and not of the form p+2^a+2^b}|>>x^{1-ε} for any ε>0, where the implied constant only depends on ε.

math.NT2009

On the periodicity of some Farhi arithmetical functions

Qing-Zhong Ji, Chun-Gang Ji

Let $k \in N$ . Let $f (x) \in Z [x]$ be any polynomial such that $f (x)$ and $f (x + 1) f (x + 2) ... f (x + k)$ are coprime in $Q [x]$ . We call $$g_{k,f}(n):=\frac{|f(n)f(n+…

Some q-congruences related to 3-adic valuations

On the number of distinct prime factors of nj+ahk

On the integers not of the form p+2a+2b

On the periodicity of some Farhi arithmetical functions

On the number of distinct prime factors of $nj + a^{h} k$

On the integers not of the form $p + 2^{a} + 2^{b}$