Question

Aratati ca nu exista numere naturale x , astfel incat fractiile 5 la puterea x +1 supra 26 si 17 supra 4 la puterea x + 1 sa fie simultan subunitare

Answer 1

[tex] \frac{ 5^{x} +1}{26}\ \textless \ 1 [/tex]
${ 5^{x} +1}\ \textless \ 26$
$5^{x} \ \textless \ 26-1$
$5^{x} \ \textless \ 25=\ \textgreater \ 5^{x}\ \textless \ 5^{2} =\ \textgreater \ x\ \textless \ 2$
$\frac{17}{4}^{x} +1\ \textless \ 1$
$17\ \textless \ 4^{x} +1=\ \textgreater \ 16\ \textless \ 4^{x} =\ \textgreater \ 4^{2} \ \textless \ 4^{x}=\ \textgreater \ x\ \textgreater \ 2$
=> solutia nu este una comuna