10b)
1+3+5+...+2011=
=1+2+3+4+5+6+...+2010+2011-2-4-6-....-2010=
=2011*2012/2-2(1+2+3+...1005)=
=2011*1006-2*1005*1006/2=
=2011*1006-1005*1006=
=1006(2011-1005)=
=1006*1006=
=1006² deci patrat perfect
11.100 < p.p<1000 p.p. apropiat de 1000 ⇒31² =961
10² < p.p<31²
p.p. sunt 11²,12².......30²
p.p.={121,144,.......900}
2000 < p.p<3000 pp apropiat de 2000 ⇒ 44²=1936
pp apropiat de 3000 ⇒ 54²=2916
44² < p.p<54²
p.p. sunt 45²,46².......53²
p.p.={2025,2116,.......2809}
12.
daca n=impar
Uc(5×(n+1)+6^n+1)+1001^(n+3)+5)=Uc(0+6+1+5)=Uc(12)=2
Uc[5×(n+1)]=0 daca n=impar
Uc[6^(n+1)]=6
Uc[1001^(n+3)]=Uc[1^(n+3)]=1
Uc[5×(n+1)]=5 daca n=par
Uc(5×(n+1)+6^n+1)+1001^(n+3)+5)=Uc(5+6+1+5)=Uc(17)=7
un numar care are ultima cifra 2 sau 7 nu este patrat perfect
