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2013-06-02T20:24:35-03:00

cara vc tmb ta na obemep e dexo pra ultima hora pra fazer a tarefa

  • Usuário do Brainly
2013-06-03T15:04:12-03:00

Pelo Algoritmo do MDC de Eiclides, temos:

 

\text{mdc}(\text{a}, \text{b})=\text{mdc}(\text{a}, \text{b}-\text{c}\times\text{a})=\text{mdc}(\text{a}, \text{r})

 

onde, \text{r}=\text{a}-\text{b}\times\text{c}

 

Logo, podemos afirmar que:

 

\text{mdc}(2^{20}-1, 2^{100}-1)=\text{mdc}(2^{20}-1, 2^{100}-1-(2^{20}-1)\times2^{80}

 

=\texrt{mdc}(2^{20}-1, 2^{80}-1)=\text{mdc}(2^{20}-1, 2^{80}-1-(2^{20}-1)\times2^{60}

 

=\text{mdc}(2^{20}-1, 2^{60}-1)=\text{mdc}(2^{20}-1, 2^{60}-1-(2^{20}-1)\times2^{40}

 

=\text{mdc}(2^{20}-1, 2^{40})=\text{mdc}(2^{20}-1, 2^{40}-1-(2^{20}-1)\times2^{20}

 

=\text{mdc}(2^{20}-1, 2^{20}-1)=\text{mdc}(2^{20}-1, 2^{20}-1)-(2^{20}-1)

 

=\text{mdc}(2^{20}-1,0)=2^{20}-1

 

Portanto, chegamos à conclusão de que, \text{mdc}(\tex{2^{100}-1, 2^{20}-1)=2^{20}-1