we are in C^3 .
(S): { ((x+y+z=2i−1 and xyz=2)),((xy+yz+xz=−2(1+i) )) :}
P(z)=z^3 +(1−2i)z^2 −2(1+i)−2.
show that (a,b,c) is solution
of (S) if and only a;b;c are
roots of P.
we define in base x the
number y and z by:
y=123^(−) ^(x ) and z=201^(−) ^x
1) without knowing x, write
the product x×y×z in function
of x.
2) we suppose that x+y+z=92
find x;y;z.
By divising an integer a by
integer b we find the result:
0.285714285714... followed
by a group of 6 digits: 285714
which is repeated indefinited.
determinate the fraction (a/b)
p ∈ Z. given:
u=14p+3 ; v=5p+1,
(E):87x+31y=2 ; we have
also the line (D): 87x−31y=2
1)show that u and v are primes
between them.(i mean the
don′t have any common divisor
excepted 1 and −1.)
2)deduct that 87 and 31 are
primes between them.
3)Solve (E).
4)Determinate points (x;y)∈ (D)
which that their cordonnates
x;y ∈ N and x≤100