Question

C ={z apartine nr nat cu proprietatea ca 2011la puterea z la a doua plus z e patrat perfect

Answer 1

∀z∈N, z*(z+1)=z²+z, numar par, 2011^(z²+z) =2011^2p =(2011^p)²
e patrat perfect
asta e toata demonstratia


de exemplu
z²+z=0
z=0
intradevar 2011^0=1 , patrat perfect

z²+z=2
z²+z-2=0
z1=1∈N   z2=-2∉N
intr-adevar 2011² e patrat perfect


z²+z=6
z²+z-6=0
z1=-3∉N, z2=2∈N
intr-adevar 2011^(4+2) =2011^6=(2011³)² patrat perfect
.............
etc