Question

Demonstrati ca(10^n+1-10^n) divide pe(5^n+1+4*5^n),pentru orice n e [N

Answer 1

[tex]10^{n+1}-10^{n}\ |\ 5^{n+1}+4*5^n\\ 10^{n+1}-10^{n}=9*10^n\\ 5^{n+1}+4*5^n=5^n(5+4)=9*5^n\\ [/tex]
Cum
$9*5^n|9*10^n$

Rezulta ca
$\ 5^{n+1}+4*5^n\ |\ 10^{n+1}-10^{n}$

si nu invers.
Eu cred ca e enuntul gresit.