7n ≡ 1 (mod 5) What is the general form of n ?


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Question Number 75186 by Hassen_Timol last updated on 08/Dec/19

$7 n \equiv 1 (\mod 5)$ $What is the general form of n ?$
Commented by mr W last updated on 08/Dec/19

$7 n = 5 m + 1$ $\Rightarrow n = 5 k + 3$
Commented by Hassen_Timol last updated on 08/Dec/19

$How do you get that from first to second$ $line, please Sir ?$
Commented by mr W last updated on 08/Dec/19

$s e e m y c o m m e n t i n Q 19198 o r h e r e :$
Commented by mr W last updated on 08/Dec/19

Commented by Hassen_Timol last updated on 08/Dec/19

$Thank you sir, may god bless you$
Commented by mr W last updated on 08/Dec/19

$s e e a l s o Q 66832 f o r o t h e r m e t h o d s$
Commented by jagannath.02 last updated on 08/Dec/19

$s i r p l e a s e s o l v e t h e t h e r m o d y n a m i c s q u e s t i o n t h a g i h a v e p o s t e d . . . p l e a s e s i r . .$
	Answered by Rio Michael last updated on 08/Dec/19

	$7 n \equiv 1 (m o d 5)$ $b y t r i a l a n d e r r o r w e l o o k f o r$ $a n u m b e r n w h i c h w h e n m u l t i p l i e d t o$ $7 g i v e s a r e m a i n d e r o f 1 w h e n d i v i d e d b y 5 .$ $s o$ $n = 1 d o e s n o t w o r k$ $n = 2 d o e s n o t w o r k$ $n = 3 \Rightarrow 7 (3) = 21$ $21 = 4 (5) + 1 r e m a i n d e r o f 1 h e n c e i t w o r k s$ $∴ n = 3 a n d w e w r i t e n \equiv 3 (m o d 5)$ $h e n c e n = 5 k + 3, k \in Z$
	Commented by Hassen_Timol last updated on 09/Dec/19

	$Thank you Sir$
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