For all integers a, b, c, m with m > 0 and c > 0, if ac ≡ bc (mod m), then a ≡ b (mod m

Question

For all integers a, b, c, m with m > 0 and c > 0, if ac ≡ bc (mod m), then a ≡ b (mod m
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Solution 1

The statement is true. Here's why:

The congruence ac ≡ bc (mod m) means that m divides ac - bc.

We can factor out c from the expression to get c(a - b). So, m divides c(a - b).

Since m > 0 and c > 0, we know that the greatest common divisor (gcd) of m and c is a positive integer.

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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