Let \( f(x)=a x^{2}+b x+c \) where \( a, b, c \in \mathbf{R} \). Su...

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Let \( f(x)=a x^{2}+b x+c \) where \( a, b, c \in \mathbf{R} \). Suppose \( f(x) \) is an integer whenever \( x \) is an integer, then which of the following are integers?
(a) \( 2 a \)
(b) \( a+b \)
(c) \( a-b \)
(d) \( c \)
E
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