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Question Number 64354 by Rio Michael last updated on 17/Jul/19

s o m e o n e w r i t e t h e s t a t e m e n t

a \equiv - a (m o d m)

s h o w t h a t t h i s s t a t e m e n t i s n o t g e n e r a l l y t r u e .! g i v i n g a c o u n t e r

e x a m p l e

Answered by MJS last updated on 17/Jul/19

49 \div 11 =

{we}^{'} re looking for the greatest n with 11 n ⩽ 49 \Rightarrow

\Rightarrow n = 4

49 \div 11 = 4

multiplicating “ {backwards}^{″}

4 \times 11 = 44

subtracting

49 \div 11 = 4

- 44

===

5 remains

now do the same here :

(- 49) \div 11 =

{we}^{'} re looking for the greatest n with 11 n ⩽ (- 49) \Rightarrow

\Rightarrow n = (- 5)

(- 49) \div 11 = (- 5)

multiplicating “ {backwards}^{″}

(- 5) \times 11 = (- 55)

subtracting

(- 49) \div 11 = (- 5)

- (- 55)

=====

6 remains

but

49 \div (- 11) = (- 4)

- 44

===

5 remains

\Rightarrow for division with remainder :

(- a) : b \neq a : (- b)

remainders are always ⩾ 0 here

but some people use different logic which

is also ok . you have to follow the same

logic throughout your work

Commented by Rio Michael last updated on 17/Jul/19

t h a n k y o u s i r

Commented by Rio Michael last updated on 17/Jul/19

i f i d e c i d e t o t a k e t h e c o u n t e r e x a m p l e

7 \equiv - 7 (m o d 6)

a n d 6 ∤ 14 s o i t s a w r o n g s t a t e m e n t ?