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What is the $gcd$ of $x+1$ and $x-1$? The euclid algorithm says that it is 2, but I'm unsure, since if I divide $x+1$ by $x-1$, the remainder is 2.

jvdhooft
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Oana
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    Depends on $x$ but since $d=\gcd (x+1,x-1)\implies d ,|,,x+1-(x-1)=2$ we see that $d$ is either $1$ or $2$. – lulu Jun 17 '17 at 20:54
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    Just to give examples: $x=3\implies d = 2$ and $x=4\implies d=1$. – lulu Jun 17 '17 at 20:55
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    Note: I assumed you meant $x$ to stand for some integer. If, instead, you meant $x\pm 1$ to denote polynomials then you need to specify what the field or ring of coefficients is. – lulu Jun 17 '17 at 20:57

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Rather, the Euclidean algorithm shows in this way that their greatest common divisor is at most $2.$ Can you figure out for which $x$ it is equal to $2$ and for which it is equal to $1$?

Cameron Buie
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