Which of the following is incorrect? If a equ | vedclass

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(D) Given $a \equiv b \pmod{m}$,we have $m \mid (a-b)$.$(i)$ For $(a+x) \equiv (b+x) \pmod{m}$,we check $(a+x) - (b+x) = a-b$. Since $m \mid (a-b)$,th

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$(a+x) \equiv (b \div x) \pmod{m}$

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(D) Given $a \equiv b \pmod{m}$,we have $m \mid (a-b)$.$(i)$ For $(a+x) \equiv (b+x) \pmod{m}$,we check $(a+x) - (b+x) = a-b$. Since $m \mid (a-b)$,this is correct.(ii) For $(a-x) \equiv (b-x) \pmod{m}$,we check $(a-x) - (b-x) = a-b$. Since $m \mid (a-b)$,this is correct.(iii) For $ax \equiv bx \pmod{m}$,we check $ax - bx = x(a-b)$. Since $m \mid (a-b)$,it follows that $m \mid x(a-b)$,so this is correct.(iv) For $(a+x) \equiv (b \div x) \pmod{m}$,this is not generally true because division is not defined in modular arithmetic in the same way as addition or multiplication,and $b \div x$ may not even be an integer. Thus,this statement is incorrect.

Which of the following is incorrect? If $a \equiv b \pmod{m}$ and $x$ is an integer,then

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