[tex]a =5\cdot 3^{42}+9^{20}-10\cdot 3^{40}\\ a = 5\cdot 3^{42}+3^{40}-10\cdot 3^{40}\\ a = 3^{40}\cdot (5\cdot 3^2+1-10)\\ a = 3^{40}\cdot (45-9)\\ a = 3^{40}\cdot 36\\a= 3^{40}\cdot 6^2\\ a = (3^{20}\cdot 6)^2\quad \checkmark[/tex]
[tex]\\[/tex]
[tex]b = 3^{42}+2^{43}\\ U(b) = U(9^{21}+2^{42}\cdot 2)\\ U(b) = U(9^{20}\cdot 9+4^{21}\cdot 2)\\ U(b) = U(81^{10}\cdot 9+16^{10}\cdot 4\cdot 2)\\ U(b) = U(1\cdot 9+6\cdot 4\cdot 2)\\ U(b) = U(57)\\ U(b) = 7\quad \checkmark\\ \\\text{Niciun patrat perfect nu se termina in 7.}[/tex]
