determiner le reste de la division eucludienne de: 10^(100) par 105


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 158906 by SANOGO last updated on 10/Nov/21

$d e t e r m i n e r l e r e s t e d e l a d i v i s i o n e u c l u d i e n n e d e :$ $10^{100} p a r 105$
	Answered by Rasheed.Sindhi last updated on 11/Nov/21

	$\underset{―}{Mod 105}$ $10^{100} = {(10^{2})}^{50} \equiv {(- 5)}^{50} = {(5^{4})}^{12} . 5^{2}$ $\equiv {(- 5)}^{12} . 5^{2} = {(5^{2})}^{6} . 5^{2} = 5^{14} = {(5^{4})}^{3} . 5^{2}$ $\equiv {(- 5)}^{3} . 5^{2} = {(- 5)}^{5} = (5^{4}) (- 5)$ $\equiv (- 5) (- 5) = 25$ $\underset{―}{Used congruences}$ $\begin{matrix} 10^{2} = 100 \equiv - 5 (m o d 105) \end{matrix}$ $\begin{matrix} 5^{4} = 25^{2} = 625 \equiv - 5 (m o d 105) \end{matrix}$
	Commented by Rasheed.Sindhi last updated on 12/Nov/21

	${Y o u}^{'} r e w e l c o m e s i r!$
	Commented by Rasheed.Sindhi last updated on 12/Nov/21

	$W h y d i d y o u d e l e t e y o u r a n s w e r s i r ?$ $I t w o u l d r e a l l y r e q u i r e s o m e$ $m i n o r c h a n g e s . T h e l o g i c w a s$ $v e r y c o r r e c t!$
	Commented by SANOGO last updated on 11/Nov/21

	$m e r c i b i e n$
	Commented by puissant last updated on 12/Nov/21

	$Y e s s i r m y l o g i c w a s c o r r e c t b u t i d i d$ $n o t a c h i e v e t h e r e s u l t i s p r o v e d t h a t$ $y o u r l o g i c i s c l e a r e r r e a l l y t h a n k y o u$ $v e r y m u c h s i r . .$
	Commented by puissant last updated on 12/Nov/21

	$T h a n k s s i r . . .$
	Commented by Rasheed.Sindhi last updated on 12/Nov/21
	��
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum