Question

Aratati ca nr 3 la puterea 2011 plus 2 ori 3 la puterea 2010 plus 3 la puterea 2009 plus 3 la puterea 2008 este patrat perfect

Answer 1

3^2008(3^3+2*3^2+3+1)=
3^2008(27+2*9+4)=
3^2008(27+18+4)=
49*3^2008
7^2*3^(2*1004)=
7^2*(3^1004)^2
(7*3^1004)^2 adica e patrat perfect

Answer 2

3²⁰¹¹+2*3²⁰¹⁰+3²⁰⁰⁹+3²⁰⁰⁸= 3²⁰⁰⁸ *(3³+2*3²+3+1)= 3²⁰⁰⁸* (27+18+3+1)=
=3²⁰⁰⁸ * 49= 3²⁰⁰⁸ * 7²=  (3¹⁰⁰⁴*7)²