Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Diophantine equation $aX^{4} - bY^{2} = 1$   As an application of the method of Thue-Siegel, we will resolve a conjecture
of Walsh to the effect that the Diophantine equation $aX^{4} - bY^2=1$, for
fixed positive integers $a$ and $b$, possesses at most two solutions in
positive integers $X$ and $Y$. Since there are infinitely many pairs $(a,b)$
for which two such solutions exist, this result is sharp.

18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con