Let a,b,c be integers. Show that if gcd, then \gcd(a,d)=\gcd(b,d)=\gcd(c,d)=1.
Here is my way of approaching this question:
Suppose \gcd(abc,d^2)=1, there exist integers x,y such that abcx+d^2y=1
a(bcx)+d(dy)=1, which implies that \gcd(a,d)=1
b(acx)+d(dy)=1, which implies that \gcd(b,d)=1
c(abx)+d(dy)=1, which implies that \gcd(c,d)=1
So far I don't really know if this is the way to answer this question. Any help would be appreciated.
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