Question

how can solve just (a) with explanation ?

Answer 1

If you have a+b= a-b (mod 5)

This means that you are searching for an integer such that a+b =a-b +5k where k in Z

a+b =a-b +5k <=> a+b-a+b=5k <=> 2b =5k…

Then you can choose any integer a.. But you have to be sure that 2b= 5k

For example… take k=2… 5k=10… then b=2

Now.. For checking :

Let a any integer.. Say a=3 for example..

Is a+2=a-2 (mod 5)?.. True

5/( a+b)-(a-b) <=> 5/2b… <=> 2b=5k..

On the other hand..

5/(a+b)+(a-b) <=>5/2a <=> 2a=5k

From this we can be confirmed that either we fix b such that 2b=5k and a would be arbitrary..

Or fix a such that 2a=5k and b would be arbitrary.




Hope it helps you...
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