   Chapter 2.5, Problem 2TFE

Chapter
Section
Textbook Problem

Label each of the following statements as either true or false. a ≡ b ( mod   n ) and c | n imply a ≡ b ( mod   c ) for c ∈ ℤ + .

To determine

Whether the statement, “ab(modn) and c|n imply ab(modc) for c+” is true or false.

Explanation

Consider the statement, “ab(modn) and c|n imply ab(modc) for c+.”

Since ab(modn) then ab=nq for some q

c|n then n=cq1 for some q1

Plug n=cq1 in ab=nq,

ab=cq1q

Since q,q</

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