Question

bună ziua! mă poate ajuta cineva la acest ex?​

Answer 1

a)

$\it A=35\cdot2^{2n}\cdot2^{-2}\cdot7^n\cdot7^{-1}\cdot224-81\cdot(4\cdot7)^n-3\cdot2^{2n}\cdot2^3\cdot7^n\cdot7=\\ \\ \\ =35\cdot(4\cdot7)^n\cdot\dfrac{224}{28}-81\cdot(4\cdot7)^n-168\cdot(4\cdot7)^n=28(35\cdot8-81-168)=\\ \\ \\ =28^n\cdot(280-249)=28^n\cdot31 \in M_{31} \Rightarrow A\ \vdots\ 31$

b)

$\it A=28^n\cdot31=14^3\cdot248\Big|_{:31} \Rightarrow 28^n=14^3\cdot8 \Rightarrow 28^n=14^3\cdot2^3 \Rightarrow\\ \\ \\ \Rightarrow 28^n=(14\cdot2)^3 \Rightarrow 28^n=28^3 \Rightarrow n=3$

Answer 2

Răspuns:

Explicație pas cu pas: