Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolution of the equation
  $(3^{x_1}-1)(3^{x_2}-1)=(5^{y_1}-1)(5^{y_2}-1)$   Consider the diophantine equation
$(3^{x_1}-1)(3^{x_2}-1)=(5^{y_1}-1)(5^{y_2}-1)$ in positive integers $x_1\le
x_2$, and $y_1\le y_2$. Each side of the equation is a product of two terms of
a given binary recurrence, respectively. In this paper, we prove that the only
solution to the title equation is $(x_1,x_2,y_1,y_2)=(1,2,1,1)$. The main
novelty of our result is that we allow products of two terms on both sides.

35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess