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An Introduction to Mathematical Reasoning by Peter J. Eccles

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20

Linear congruences

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In this chapter we discuss the following problem.

Problem 20.0.1 Given a positive integer m and integers a and b, solve the congruence

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i.e. find all integers x which satisfy this congruence.

Such a problem is called a linear congruence and examples have already been considered in the previous chapter. In this chapter we will discuss the general solution. We will make use of a close relationship between this problem and the linear diophantine equation problem discussed in Chapter 18.

20.1 A criterion for the existence of ...

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