Let $h, k, l$ be three co-prime integers. Can we always find a set of integers $n_1, n_2, n_3$ such that $n_1 h + n_2 k + n_3 l = 1$ ? Thanks.
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Do you know how to show this for $2$ coprime integers? Have you tried just extending that argument? – lulu Aug 12 '17 at 19:14
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@Ahmad I assume (but am not sure) that the OP means that the three numbers are jointly coprime. That is, that there is no $d>1$ which divides each of the three. They need not be pairwise coprime. – lulu Aug 12 '17 at 19:19
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@lulu Yes. They need not be pariwise coprimes. – user3499383 Aug 12 '17 at 19:23