Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On harmonic numbers and Lucas sequences   Harmonic numbers $H_k=\sum_{0<j\le k}1/j (k=0,1,2,...)$ arise naturally in
many fields of mathematics. In this paper we initiate the study of congruences
involving both harmonic numbers and Lucas sequences. One of our three theorems
is as follows: Let u_0=0, u_1=1, and u_{n+1}=u_n-4u_{n-1} for n=1,2,3,....
Then, for any prime p>5 we have $$\sum_{k=0}^{p-1}u_{k+\delta}H_k/2^k=0 (mod
p),$$ where $\delta=0$ if p=1,2,4,8 (mod 15), and $\delta=1$ otherwise.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph