Explain please?

#1

if (b-a)%m=0 then how can we conclude b%m=a%m

#2

This is a simple observation in maths.
Let’s go other way, let x= a%m , y=b%m.
You know that if( a-b)%m =0.
You can do (a+m -b+m)%m =0.
Open brackets and (a+m)%m - (b+m)%m =0.
So take second term to right side and you can prove the following

#3

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