a) 5|n
atunci , n=5k
[25k²/5]+[(25k²+10k+1)/5]+[(25k²+20k+4)/5]+
[(25k²+30k+9)/5]+[(25k²+40k+16)/5]=
5k²+5k²+2k+5k²+4k+5k²+6k+1+5k²+8k+3=25k²+20k+4=(5k+2)², patrat perfect
b) presupunem
n=5k+1
[(25k²+10k+1)/5]+[(25k²+20k+4)/5]+[(25k²+30k+9)/5]+[(25k²+40k+16)/5]+
[25(k+1)²/5]=
5k²+2k+5k²+4k+5k²+6k+1+5k²+8k+3+5(k+1)²=20k²+20k+4+5k²+10k+5=
25k²+30k+9=(5k+3)², p.p
analog procedezi si pt n=5k+2 probabil iti va rezulta (5k+4)²
n=5k+3 probabil iti va rezulta (5(k+1))²
n=5k+4 probabil iti va rezulta(5(k+1)+1)²
