n²+n+9 = patrat perfect
n²+n+9 =x²
(x+n)(x-n) = n+9
x+n = 1 x = 1-n
x-n = n+9 x = 2n+9 1-n = 2n +9 3n = -8 n = -8/3
n² + n + 9 = 64/9 - 8/3 + 9 = (64 -24+81)/9 = 121/9 = (11/3)² = p.p.
x+n = n +9 x = 9
x - n = 1 n = x -1 = 8
n²+ n +9 = 64 +8 + 9 = 81= 9² = p.p.
raspuns : n ∈ {-8/3, 8}
