Here Is a Sample Proof That Contains an Error $a \mid b$

question 109

Essay

Here is a sample proof that contains an error. Explain why the proof is not correct.
Theorem: If $a \mid b$ and $b \mid c$ , then $a \mid c$ .
Proof: Since $a \mid b , b = a k$ .
Since $b \mid c , c = b k$ .
Therefore $c = b k = ( a k ) k = a k ^ { 2 }$ .
Therefore $a \mid c$ .

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