Let $(a;b) = 1$ and $c > 0$. Prove that there is an integer n such that $(a+bn;c) = 1$ where $(a,b)=\gcd(a,b)$
Let $(a;b) = 1$ and $c > 0$. Prove that there is an integer n such that $(a+bn;c) = 1$
1
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elementary-number-theory
greatest-common-divisor
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0Show us what you have tried. – 2017-01-30
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0Let $n$ be the product of all the primes that divide $c$ but not $a$. – 2017-01-30
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0What are your thoughts? What have you tried? Where are you stuck? You need to [provide context](http://meta.math.stackexchange.com/questions/9959/how-to-ask-a-good-question/9960#9960) for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help. – 2017-01-30
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0@Greg, this question came up when I was writing my PhD thesis; Schinzel showed me how to do it. – 2017-01-30