For the following statement, either prove that they are true or provide a counterexample:Let a, b, c, m in Z such that m > 1. If ac -= bc (mod m), then a -= b (mod m)

glasskerfu 2021-02-25 Answered

For the following statement, either prove that they are true or provide a counterexample:
Let a, b, c, mZ such that m > 1. If acbc(mod),then ab(modm)

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Expert Answer

Cullen
Answered 2021-02-26 Author has 89 answers

Let a, b, c, mZ such that m > 1. If acbc(modm),then ab(modm)
This statement is false.
Counterexample:
44
41612
By using definition of congruence,
1216mod(4)
Now,
12=62 and 16=82
6282mod(4)
Compare it with acbc(modm),
We get c = 2.
But 6!8mod(4)
as 4!86
Therefore, If acbc(modm),then ab(modm) is false.

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