Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation of $\frac{1}{2}(F_n-1)(F_{n+1}-1)$ and
  $\frac{1}{2}(F_n-1)(F_{n+2}-1)$   Let $a, b\in \mathbb{N}$ be relatively prime. We consider $(a-1)(b-1)/2$,
which arises in the study of the $pq$-th cyclotomic polynomial, where $p,q$ are
distinct primes. We prove two possible representations of $(a-1)(b-1)/2$ as
nonnegative, integral linear combinations of $a$ and $b$. Surprisingly, for
each pair $(a,b)$, only one of the two representations exists and the
representation is also unique. We then investigate the representations of
$(F_n-1)(F_{n+1}-1)/2$ and $(F_n-1)(F_{n+2}-1)/2$, where $F_i$ is the $i^{th}$
Fibonacci number, and observe several nice patterns.

17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an