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Determine necessary and sufficient conditions on x and c so that the following holds

Chapter 1, Problem 1.15

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QUESTION:

Determine necessary and sufficient conditions on x and c so that the following holds: for any a, b,if ax bx mod c, then a b mod c.

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QUESTION:

Determine necessary and sufficient conditions on x and c so that the following holds: for any a, b,if ax bx mod c, then a b mod c.

ANSWER:

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Here is determined the necessary and sufficient condition on x and c for the statement if   it means  is a multiple of c, therefore .

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