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Classify each of the following statements as true or false. (a) 24 3 (mod 7). (b) 17 9

Chapter 7, Problem 2

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QUESTION:

Classify each of the following statements as true or false. (a) 24 3 (mod 7). (b) 17 9 (mod 8). (c) 5 5 (mod 4). (d) 24 3 (mod 3).

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QUESTION:

Classify each of the following statements as true or false. (a) 24 3 (mod 7). (b) 17 9 (mod 8). (c) 5 5 (mod 4). (d) 24 3 (mod 3).

ANSWER:

Step 1 of 5

For integers \(a\) and \(b\), \(a\) is not equal to zero means \(a\) divides \(b\)  if \(b=ac\) for some integer \(c\). If \(a\ |\ b\)  then \(a\) is called a factor or a divisor of \(b\), and \(b\) is called multiple of \(a\). The integer \(a\) is congruent to \(b\) modulo \(n\) if \(n(a-b)\). It is indicated as \(a\equiv b(mod\ n)\) and if the integer \(a\) is not congruent to \(b\) modulo \(n\) then it is indicated as \(a\not\equiv b(mod\ n)\).

 

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