Question

a=9 la puterea 2016 - 7 la puterea 2012 a se divide cu 10?

Answer 1

a = 9^2016 - 7^2012

U(9^2016) = 1

9 la o putere para are intotdeauna ultima cifra 1 . (2016 este un numar par)

U(7^2012) = U(7^4) = U(2401) = 1

U(a) = U(1 - 1) = 0

Asadar,
orice numar care se termina in 0 se divide cu 10 .

Answer 2

 

[tex] \displaystyle\\ U(A)=U\left(9^{2016}\right) - U\left(7^{2012}\right)=\\\\ =U\left(9^{2\times1008}\right) - U\left(7^{4\times 503}\right)=\\\\ =U\left(\Big(9^2\Big)^{1008}\right) - U\left(\Big(7^4\Big)^{503}\right)=\\\\ =U\left(81^{10\B08}\right) - U\left(2401^{503}\right)=\\\\ =U\left(1^{10\B08}\right) - U\left(1^{503}\right)=1 - 1 = 0\\\\ U(A)=0\\\\ \text{Ultima cifra a lui A este zero.}\\\\ \Longrightarrow~~ \boxed{\bf A~\vdots~10}~~~\text{(A este divizibil cu 10)} [/tex]