Question

Determină ultima cifra a numarului 3⁹+2⁹+5⁹.​

Answer 1

 

$\displaystyle\bf\\U\left(3^9+2^9+5^9\right)=\\\\=U\left(U\Big(3^9\Big)+U\Big(2^9\Big)+U\Big(5^9\Big)\right)=\\\\=U\left(U\Big(3^{4\times2+1}\Big)+U\Big(2^{4\times2+1}\Big)+U\Big(5^9\Big)\right)=\\\\=U\left(U\Big(\Big(3^4\Big)^2\times3}\Big)+U\Big(\Big(2^4\Big)^2\times2}\Big)+U\Big(5^9\Big)\right)=\\\\=U\left(U\Big(81^2\times3}\Big)+U\Big(16^2\times2}\Big)+U\Big(5^9\Big)\right)=\\\\=U\left(U\Big(1\times3}\Big)+U\Big(6\times2}\Big)+5\right)=$

 

$\displaystyle\bf\\=U\left(U\Big(3}\Big)+U\Big(12}\Big)+5\right)=\\\\=U\Big(3+2+5\Big)=U\Big(10\Big)=\boxed{\bf0}$

 

Answer 2

U(3⁹ + 2⁹ + 5⁹) =

= U(3⁸·3 + 2⁸·2 + 5) =

= U[(3⁴)²·3 + (2⁴)²·3 + 5) =

= U(81²·3 + 16²·2 + 5) =

= U(1·3 + 6·2 + 5) =

= U(20) =

= 0