Réseaux et aires Parimaths

V V
R2O V
R
X V
X R X
N S X V
S N R
S N X V
N R S
X
X R
I(X)F(X)R X
XA(X)X I(X)F(X)
A(X)
I(X)F(X)

X g
X
X O r N(r)R
X
N(5)
N(r)r
r π r−√22≤N(r)≤πr+√22.
pN(r)−√2π2
≤ A(X)≤pN(r) + √2π2 .
n T (n)
m≤n x2+y2=m
n > 0T(n)>n
5

X
X V A(X)
A(X)X
R
A(a1, a2)B(b1, b2)V A +B
(a1+b1, a2+b2)−A(−a1,−a2)s sA
(sa1, sa2)
A(1,2) B(3,−3) C=A+B D =−A E =A+ (−B)
F= (2A)−(1
3B)
A(X)>1C
D X C + (−D)∈R
X
X X
A(X)>4X R
A(X)>4
A(a1, a2)B(b1, b2)V
OAB 1
2|a1b2−a2b1|
O A B
(O, A, B)V
sA +tB s t V
A B C m n
C=mA +nB R(A, B)R(A, B)
C s t [0,1[ C=sA+tB
R(A, B)
A(1,0) B(0,1)
A(2,−1) B(3,1)
R(A, B) (x, y)x y x ≡3y
mod 5
m n A B
(x, y)x≡my mod n
A B R(A, B)
R

A1(1,0) B1(0,1)
A2(1,1) B2(0,1)
A3(1,1) B3(1,2)
A4(2013,−2012) B4(−2014,2013)
x2−dy2= 1
p
x x2≡1 mod p p