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I have encountered a question asked by my friend, which is stated as follows:

Suppose there exists integers a, b, c, k, l, m such that $ka+lb+mc=1$, then, is the following statement true?

"There exists at least one pair from $(a, b)$, $(b,c)$,$(a,c)$ that is coprime."

Personally, I think the statement is plausible as I can assume one of k, l, and m is zero, which would mean that there exists one pair of coprime numbers. However, I have difficulty in proving it strictly. Many thanks for your help.

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It is false. Example: $$10+6-15=1$$

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  • $\begingroup$ thank you...very clear answer $\endgroup$ – Jamie Carr Oct 21 '18 at 17:19

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