n²-2n+16 = patrat perfect
n²-2n+16 =x²
x²-n²=16-2n
(x+n)(x-n) = 16-2n =1×2(8-n)
x+n = 2 x = 2-n
x-n = 8-n x = 8 2-n = 8 n =-6
n² - 2n + 16 = (-6)² - 2×(-6)+16 = 36 +12+16 =64= (8)² = p.p.
x-n = 2 x = 2+n
x+n =8-n x = 8-2n 2+n = 8-2n 3n = 6 n=2
n² - 2n + 16 = (2)² - 2×(2)+16 = 4 -4+16 =16= (4)² = p.p.
-2n+16=0 ⇒ n= 8
n² - 2n + 16 = (8)² - 2×(8)+16 = 64 -16+16 =64= (8)² = p.p.
raspuns : n ∈ {-6,2,8}
