论文标题
Adamchuk的猜想的证明
Proof of a conjecture of Adamchuk
论文作者
论文摘要
在本文中，我们证明了一个一致性，证实了Adamchuk的猜想。对于任何prime $ p \ equiv1 \ pmod3 $和$ a \ in \ mathbb {z}^{+} $，我们有\ begin {align*} \ sum_ {k = 1}^{\ frac {\ frac {2} 3（p^a-a-1）} \ binom} \ binom \ end {align*}
In this paper, we prove a congruence which confirms a conjecture of Adamchuk. For any prime $p\equiv1\pmod3$ and $a\in\mathbb{Z}^{+}$, we have \begin{align*} \sum_{k=1}^{\frac{2}3(p^a-1)}\binom{2k}k\equiv0\pmod{p^2}. \end{align*}
