Dawson Macdonald
12/16/2023 · Elementary School
If \( a \) and \( b \) are integers then \( a \) divides \( b \) if there exists an integer \( c \) such that \( a=b c \). \( a=b c \) for some integer \( c \). \( b=a c \) for some itteger \( c \). there exists an integer \( c \) such that \( b=a c \).
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Step-by-step Solution
The correct statement for the definition of divisibility is:
**\( a \) divides \( b \) if there exists an integer \( c \) such that \( b = a c \).**
This means that \( b \) can be expressed as \( a \) multiplied by some integer \( c \). In other words, \( b \) is a multiple of \( a \).
So, the correct option from your list is:
**there exists an integer \( c \) such that \( b = a c \).**
Quick Answer
The correct statement is: there exists an integer \( c \) such that \( b = a c \).
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