TD 1 Exercice VI. On appelle nombres premiers jumeaux un couple

13215 721 1183
143 6435
a, b, d d 2a+b
3a+ 2b d a b
a, b, m 1m
2a+b3a+ 2b m a b
x y d
x=dx1y=dy1
d= (x, y)x1y1
(7696; 4144)
(7696; 4144)
a, b, c ∈Zm≥0
a b Zambmm.
p amp a
p
a b c (a, b) = 1, ab c.
(a, b)6= 1
(p, p + 2)
p≥5p+ 2
p+p+ 2
p, p + 2, p + 4
a= 23×32×132
a
a
a
b=pα1
1× ··· × pαn
npi
αi∈N∗

n
6 = 1+2+3 28 = 1+2+4+7+14
p2p−1n= 2p−1(2p−1)
a∈Z(14a+ 3,21a+ 4) = 1 (9a+ 4,2a−1) ∈
{1; 17}
a b
a2= 2b2√2
ln 7
ln 5
Fn= 22n+ 1, n ≥0
F0, F1, F2, F3F4.
641 F5
2m+ 1 m= 2n2m+ 1
a b
Z×Z(E)ax +by = 1
(x0, y0) (E)
(E){(x0−kb, y0+ka)|k∈Z}
Z×Z314x−159y= 1
Z×Z N ×N39x+ 21y= 6
x y 1900 + z,
u v
N.
3
√N+uvwxyz = 11 888 815.
1≤x≤31
x=c`···c0x∈N
x=c`10`+··· + 10c1+c0
x≡(−1)`c`+··· + (−1)ici··· − c1+c0( 11)
641489 42813617 3 9 11
A= 20092009 B A C B D
C D
n∈Z169 -n2+ 20n+ 74
n∈N9|22n+ 15n−1