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Theorem

If a≡ bmod ...

Question

If $a \equiv b (m o d m)$ and $x$ is an integer, then which of the following is incorrect?

(a + x) \equiv (b + x) (m o d m)

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(a - x) \equiv (b - x) (m o d m)

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a x \equiv b x (m o d m)

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(a \div x) \equiv (b \div x) (m o d m)

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Solution

The correct option is B $(a \div x) \equiv (b \div x) (m o d m)$
A, B and C be the correct option.
All these are the properties of congruence.
Only D is not the properties of congruence.

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