let give the sequence (y_n ) /y_0 (x)=1 and
y_n (x)= 1+ ∫_0 ^x (y_(n−1) (t))^2 dt , let suppose x∈[0,1] prove
that (y_n ) is increasing majored by (1/(1−x)) if y=lim_(n→+∞) y_n
prove that y is solution of differencial equation
y^, =y^2 and y(o)=1.
let give a prime number p>2 and a /D(a,p)=1 and
suppose that the equation x^2 ≡ a[p]have a solution1)
1) prove that a^((p−1)/2) ≡ 1 [p]
2)prove that x^2 ≡ −1[p] ⇔ p≡ 1 [4]