Dúvida sobre Resíduos

["Marcos Eike Tinen dos Santos" <mjsanto@xxxxxxxxxxxxxxxxx>]

Veja:

Complete system of Residues

a) numbers which are congruent modulo m form an equivalence class modulo m.
(aqui tudo bem, lógico)

.....

Any number of an equivalence class is said  to be a residue modulo m with
respect to all the numbers of the equivalence class. The residue obtained
for q = 0 is equal to the remainder r itself, and is called the least
non-negative residue.
The residue p smallest absolute  value is called the absolutely least
residue.

Pessoal q vem da definição de que : we obtain all the numbes of an
equivalence class is we let q in the form mq + r run throught all the
integers.

Alguem poderia me explicar o que eu descrevi, não entendi corretamente, e
posso estar perdendo algumas propriedades.

2) Problema:

Let T be the number of lattice points (x,y) of the region x^2 + y^2 <= r^2
(r>=2) prove que:

T = (pi)r^2 + O[r^(2/3) * ln r]

Ats,
Marcos Eike