He-Xia Ni

activity

20162026

most citedSome

q

-congruences arising from certain identities

3 citations · 10 across the 17 of their papers we have counts for

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Showing 2018Show all

2 papers · 1 filter

math.NT2018

Divisibility of some binomial sums

He-Xia Ni, Hao Pan

With help of $q$ -congruence, we prove the divisibility of some binomial sums. For example, for any integers $ρ, n \geq 2$ , $$\sum_{k=0}^{n-1}(4k+1) \binom{2k}{k}^ρ\cdot (-4)^{ρ(n-1-k…

math.NT2018

On the almost universality of $⌊ x^{2} / a ⌋ + ⌊ y^{2} / b ⌋ + ⌊ z^{2} / c ⌋$

Hai-Liang Wu, He-Xia Ni, Hao Pan

In 2013, Farhi conjectured that for each $m \geq 3$ , every natural number $n$ can be represented as $⌊ x^{2} / m ⌋ + ⌊ y^{2} / m ⌋ + ⌊ z^{2} / m ⌋$ with $x,y,z\in\Z…

Divisibility of some binomial sums

On the almost universality of ⌊x2/a⌋+⌊y2/b⌋+⌊z2/c⌋

On the almost universality of $⌊ x^{2} / a ⌋ + ⌊ y^{2} / b ⌋ + ⌊ z^{2} / c ⌋$