Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Observations on a certain theorem of Fermat and on others concerning
  prime numbers   E26 in the Enestrom index. Translated from the Latin original, "Observationes
de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus"
(1732).
  In this paper Euler gives a counterexample to Fermat's claim that all numbers
of the form 2^{2^m}+1 are primes, by showing 2^{2^5}+1=4294967297 is divisible
by 641. He also considers many cases in which we are guaranteed that a number
is composite, but he notes clearly that it is not possible to have a full list
of circumstances under which a number is composite. He then gives a theorem and
several corollaries of it, but he says that he does not have a proof, although
he is sure of the truth of them. The main theorem is that a^n-b^n is always
able to be divided by n+1 if n+1 is a prime number and both a and b cannot be
divided by it.

37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph