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a fost răspuns

Aratati ca pentru orice n natural:
7 | (2^n+2 + 2^n+1 + 2^n ) . Va roogg

Răspuns :

Malinaclim
[tex] 2^{n+2}+2^{n+1}+2^{n}= 2^{n}*( 2^{2}+2+1)=2^{n}*(4+2+1)=7*2^{n} [/tex]
=> 7 | [tex] 2^{n+2}+2^{n+1}+2^{n} [/tex]
Mihai243
2^n+2+2^n+1+2^n=2^n(2²+2¹+1)=2^n+7
7|(2^n+7)
7|7
7|(2^n+2+2^n+1+2^n)