2^2 = 4
2^2^2 = 8
2^2^2^2 = 16
2^2^2^2^2=32
2^2^2^2^2^2=64 deci se repeta ultimele cifra 4,8,6,2
2004 : 4 = 501 deci ulima cifra pentru 2^2004 =2
1+1+2+2=6
2005+2x(1+2+3....2004) = 2005+2x 2004(2004+1)/2= 2005+2004*2005=2005(2004+1) = 2005² deci patrat perfect