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Given that k is a positive integer less than 6, how many values can k take on such that 3x=k (mod 6) has no solutions in x?

 Dec 9, 2018
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\(k \in \{1,2,3,4,5\}\\ 3x = k \pmod{6} \\ \text{I guess you are assuming }x \text{ is an integer as well?} \)

 

\(x \text{ even } \Rightarrow 3x \pmod{6} = 0\\ x \text{ odd } \Rightarrow 3x \pmod{6} = 3\\ \text{ so }k = 1,2,4,5\\ \text{has no solutions for }x \in \mathbb{Z}\)

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 Dec 9, 2018

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