number of coprimes to a less than b Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Count Integers Not Greater Than $a$ Coprime To $b$Variation on euler totient/phi functionCo Prime Numbers less than NNumber of coprimes of $n$ divisible by 3Calculation of product of all coprimes of number less than itselfHow to count the number of perfect square greater than $N$ and less than $N^2$ that are relatively prime to $N$?All numbers less than 100 with phi(n) = 64How many numbers less than $m$ and relatively prime to $n$, where $m>n$?Number of integers (less than $n$) that are divisible by a prime factor of $n$Are there any known methods for finding Upper/Lower bounds on the number of Totients of x less than another number y?Find taxicab numbers in less than $O(n^2)$ time with number theory into consideration
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number of coprimes to a less than b
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Count Integers Not Greater Than $a$ Coprime To $b$Variation on euler totient/phi functionCo Prime Numbers less than NNumber of coprimes of $n$ divisible by 3Calculation of product of all coprimes of number less than itselfHow to count the number of perfect square greater than $N$ and less than $N^2$ that are relatively prime to $N$?All numbers less than 100 with phi(n) = 64How many numbers less than $m$ and relatively prime to $n$, where $m>n$?Number of integers (less than $n$) that are divisible by a prime factor of $n$Are there any known methods for finding Upper/Lower bounds on the number of Totients of x less than another number y?Find taxicab numbers in less than $O(n^2)$ time with number theory into consideration
$begingroup$
We know that number of coprimes less than a number can be found using euler function https://brilliant.org/wiki/eulers-totient-function/ But if there are two numbers p,q and we need to find number of numbers less than q and coprime to p. Is there any efficient method ? can we develop an algorithm.
number-theory prime-numbers algorithms prime-factorization totient-function
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
$endgroup$
|
show 2 more comments
$begingroup$
We know that number of coprimes less than a number can be found using euler function https://brilliant.org/wiki/eulers-totient-function/ But if there are two numbers p,q and we need to find number of numbers less than q and coprime to p. Is there any efficient method ? can we develop an algorithm.
number-theory prime-numbers algorithms prime-factorization totient-function
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
$endgroup$
1
$begingroup$
Which is greater, $p$ or $q$? It does matter.
$endgroup$
– ajotatxe
Apr 2 at 17:41
$begingroup$
We have both the cases. p<q and p>q as well.
$endgroup$
– Manoharsinh Rana
Apr 2 at 17:42
1
$begingroup$
Answered here: math.stackexchange.com/a/3158036/181098
$endgroup$
– W-t-P
Apr 2 at 18:02
$begingroup$
@W-t-P Can you give a simple,actual example how to calculate ?
$endgroup$
– Manoharsinh Rana
Apr 2 at 18:14
1
$begingroup$
You have a very explicit formula: $sum_dmid a mu(d) lfloor b/drfloor$. Here $d$ runs over all positive divisors of $a$ (including $1$ and $a$), $mu$ is the Mobious function, and $lfloor b/drfloor$ is the largest integer not exceeding $b/d$. I am afraid I cannot explain anything beyond this.
$endgroup$
– W-t-P
Apr 2 at 18:38
|
show 2 more comments
$begingroup$
We know that number of coprimes less than a number can be found using euler function https://brilliant.org/wiki/eulers-totient-function/ But if there are two numbers p,q and we need to find number of numbers less than q and coprime to p. Is there any efficient method ? can we develop an algorithm.
number-theory prime-numbers algorithms prime-factorization totient-function
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
$endgroup$
We know that number of coprimes less than a number can be found using euler function https://brilliant.org/wiki/eulers-totient-function/ But if there are two numbers p,q and we need to find number of numbers less than q and coprime to p. Is there any efficient method ? can we develop an algorithm.
number-theory prime-numbers algorithms prime-factorization totient-function
number-theory prime-numbers algorithms prime-factorization totient-function
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
asked Apr 2 at 17:38
Manoharsinh RanaManoharsinh Rana
116
116
1
$begingroup$
Which is greater, $p$ or $q$? It does matter.
$endgroup$
– ajotatxe
Apr 2 at 17:41
$begingroup$
We have both the cases. p<q and p>q as well.
$endgroup$
– Manoharsinh Rana
Apr 2 at 17:42
1
$begingroup$
Answered here: math.stackexchange.com/a/3158036/181098
$endgroup$
– W-t-P
Apr 2 at 18:02
$begingroup$
@W-t-P Can you give a simple,actual example how to calculate ?
$endgroup$
– Manoharsinh Rana
Apr 2 at 18:14
1
$begingroup$
You have a very explicit formula: $sum_dmid a mu(d) lfloor b/drfloor$. Here $d$ runs over all positive divisors of $a$ (including $1$ and $a$), $mu$ is the Mobious function, and $lfloor b/drfloor$ is the largest integer not exceeding $b/d$. I am afraid I cannot explain anything beyond this.
$endgroup$
– W-t-P
Apr 2 at 18:38
|
show 2 more comments
1
$begingroup$
Which is greater, $p$ or $q$? It does matter.
$endgroup$
– ajotatxe
Apr 2 at 17:41
$begingroup$
We have both the cases. p<q and p>q as well.
$endgroup$
– Manoharsinh Rana
Apr 2 at 17:42
1
$begingroup$
Answered here: math.stackexchange.com/a/3158036/181098
$endgroup$
– W-t-P
Apr 2 at 18:02
$begingroup$
@W-t-P Can you give a simple,actual example how to calculate ?
$endgroup$
– Manoharsinh Rana
Apr 2 at 18:14
1
$begingroup$
You have a very explicit formula: $sum_dmid a mu(d) lfloor b/drfloor$. Here $d$ runs over all positive divisors of $a$ (including $1$ and $a$), $mu$ is the Mobious function, and $lfloor b/drfloor$ is the largest integer not exceeding $b/d$. I am afraid I cannot explain anything beyond this.
$endgroup$
– W-t-P
Apr 2 at 18:38
1
1
$begingroup$
Which is greater, $p$ or $q$? It does matter.
$endgroup$
– ajotatxe
Apr 2 at 17:41
$begingroup$
Which is greater, $p$ or $q$? It does matter.
$endgroup$
– ajotatxe
Apr 2 at 17:41
$begingroup$
We have both the cases. p<q and p>q as well.
$endgroup$
– Manoharsinh Rana
Apr 2 at 17:42
$begingroup$
We have both the cases. p<q and p>q as well.
$endgroup$
– Manoharsinh Rana
Apr 2 at 17:42
1
1
$begingroup$
Answered here: math.stackexchange.com/a/3158036/181098
$endgroup$
– W-t-P
Apr 2 at 18:02
$begingroup$
Answered here: math.stackexchange.com/a/3158036/181098
$endgroup$
– W-t-P
Apr 2 at 18:02
$begingroup$
@W-t-P Can you give a simple,actual example how to calculate ?
$endgroup$
– Manoharsinh Rana
Apr 2 at 18:14
$begingroup$
@W-t-P Can you give a simple,actual example how to calculate ?
$endgroup$
– Manoharsinh Rana
Apr 2 at 18:14
1
1
$begingroup$
You have a very explicit formula: $sum_dmid a mu(d) lfloor b/drfloor$. Here $d$ runs over all positive divisors of $a$ (including $1$ and $a$), $mu$ is the Mobious function, and $lfloor b/drfloor$ is the largest integer not exceeding $b/d$. I am afraid I cannot explain anything beyond this.
$endgroup$
– W-t-P
Apr 2 at 18:38
$begingroup$
You have a very explicit formula: $sum_dmid a mu(d) lfloor b/drfloor$. Here $d$ runs over all positive divisors of $a$ (including $1$ and $a$), $mu$ is the Mobious function, and $lfloor b/drfloor$ is the largest integer not exceeding $b/d$. I am afraid I cannot explain anything beyond this.
$endgroup$
– W-t-P
Apr 2 at 18:38
|
show 2 more comments
0
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1
$begingroup$
Which is greater, $p$ or $q$? It does matter.
$endgroup$
– ajotatxe
Apr 2 at 17:41
$begingroup$
We have both the cases. p<q and p>q as well.
$endgroup$
– Manoharsinh Rana
Apr 2 at 17:42
1
$begingroup$
Answered here: math.stackexchange.com/a/3158036/181098
$endgroup$
– W-t-P
Apr 2 at 18:02
$begingroup$
@W-t-P Can you give a simple,actual example how to calculate ?
$endgroup$
– Manoharsinh Rana
Apr 2 at 18:14
1
$begingroup$
You have a very explicit formula: $sum_dmid a mu(d) lfloor b/drfloor$. Here $d$ runs over all positive divisors of $a$ (including $1$ and $a$), $mu$ is the Mobious function, and $lfloor b/drfloor$ is the largest integer not exceeding $b/d$. I am afraid I cannot explain anything beyond this.
$endgroup$
– W-t-P
Apr 2 at 18:38