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With reference to this question, I am trying to generalize my previous question here.

If I have two GCD equations with common variable $m$ as follow: $GCD(m,p_i)=1$ and $GCD(m+7,p_i)=1$ where $p_i$ takes values from the first 20 prime numbers. can the two GCD equations be combined (since they both share second argument $p_i$)?

My target is to get all potential values of $m$ (in a given range, say from 1 to 1000). I thought if we can combine the two GCD equations into one GCD equation (for each $p_i$) then we have probably good base to calculate all values of m.

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  • $\begingroup$ $\gcd(m,p_i)=1$ and $\gcd(m+7,p_i)=1$ combine to give $\gcd(m(m+7),p_i)=1$. $\endgroup$ – Gerry Myerson Aug 18 '17 at 0:22
  • $\begingroup$ @GerryMyerson, OH yes, this is allowed! thanks a lot.! $\endgroup$ – bijan karimi Aug 18 '17 at 0:50

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