solving-set-of-gcd-equations (continued discussion)
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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.
prime-numbers systems-of-equations greatest-common-divisor
edited Nov 21 at 13:35
Klangen
1,36511231
asked Aug 17 '17 at 18:09
bijan karimi
144
add a comment |
up vote
0
down vote
favorite
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.
prime-numbers systems-of-equations greatest-common-divisor
edited Nov 21 at 13:35
Klangen
1,36511231
asked Aug 17 '17 at 18:09
bijan karimi
144
$gcd(m,p_i)=1$ and $gcd(m+7,p_i)=1$ combine to give $gcd(m(m+7),p_i)=1$.
– Gerry Myerson
Aug 18 '17 at 0:22
@GerryMyerson, OH yes, this is allowed! thanks a lot.!
– bijan karimi
Aug 18 '17 at 0:50
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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.
prime-numbers systems-of-equations greatest-common-divisor
edited Nov 21 at 13:35
Klangen
1,36511231
asked Aug 17 '17 at 18:09
bijan karimi
144
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.
prime-numbers systems-of-equations greatest-common-divisor
prime-numbers systems-of-equations greatest-common-divisor
edited Nov 21 at 13:35
Klangen
1,36511231
asked Aug 17 '17 at 18:09
bijan karimi
144
edited Nov 21 at 13:35
Klangen
1,36511231
asked Aug 17 '17 at 18:09
bijan karimi
144
edited Nov 21 at 13:35
Klangen
1,36511231
edited Nov 21 at 13:35
Klangen
1,36511231
edited Nov 21 at 13:35
Klangen
1,36511231
1,36511231
asked Aug 17 '17 at 18:09
bijan karimi
144
asked Aug 17 '17 at 18:09
bijan karimi
144
asked Aug 17 '17 at 18:09
bijan karimi
144
144
$gcd(m,p_i)=1$ and $gcd(m+7,p_i)=1$ combine to give $gcd(m(m+7),p_i)=1$.
– Gerry Myerson
Aug 18 '17 at 0:22
@GerryMyerson, OH yes, this is allowed! thanks a lot.!
– bijan karimi
Aug 18 '17 at 0:50
add a comment |
$gcd(m,p_i)=1$ and $gcd(m+7,p_i)=1$ combine to give $gcd(m(m+7),p_i)=1$.
– Gerry Myerson
Aug 18 '17 at 0:22
@GerryMyerson, OH yes, this is allowed! thanks a lot.!
– bijan karimi
Aug 18 '17 at 0:50
$gcd(m,p_i)=1$ and $gcd(m+7,p_i)=1$ combine to give $gcd(m(m+7),p_i)=1$.
– Gerry Myerson
Aug 18 '17 at 0:22
$gcd(m,p_i)=1$ and $gcd(m+7,p_i)=1$ combine to give $gcd(m(m+7),p_i)=1$.
– Gerry Myerson
Aug 18 '17 at 0:22
@GerryMyerson, OH yes, this is allowed! thanks a lot.!
– bijan karimi
Aug 18 '17 at 0:50
@GerryMyerson, OH yes, this is allowed! thanks a lot.!
– bijan karimi
Aug 18 '17 at 0:50
add a comment |
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$gcd(m,p_i)=1$ and $gcd(m+7,p_i)=1$ combine to give $gcd(m(m+7),p_i)=1$.
– Gerry Myerson
Aug 18 '17 at 0:22
@GerryMyerson, OH yes, this is allowed! thanks a lot.!
– bijan karimi
Aug 18 '17 at 0:50