Question

Aflați ulrima cifra a numarului a. Rapid va rog! ​

Answer 1

 

$\displaystyle\bf\\U(a)=ultima~cifra~a~lui~a=\\\\=U\Big(2016^{2017}+2014^{2017}+2012^{2017}\Big)=\\\\=U\Big(6^{2017}+4^{2017}+2^{2017}\Big)=\\\\=U\Big(6^{2017}+4^{2\times1008+1}+2^{4\times504+1}\Big)=\\\\=U\Big(6^{2017}+\Big(4^2\Big)^{1008}\times4^1+\Big(2^4\Big)^{504}\times2^1\Big)=\\\\=U\Big(6^{2017}+16^{1008}\times4^1+16^{504}\times2^1\Big)=\\\\=U\Big(6^{2017}+6^{1008}\times4+6^{504}\times2\Big)=\\\\=U\Big(6+6\times4+6\times2\Big)=\\\\=U\Big(6+24+12\Big)=U(42)=\boxed{\bf2}$