How do I break down the math symbols in this equation












2












$begingroup$



$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$




How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?






notation







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
    $endgroup$
    – Minus One-Twelfth
    2 hours ago












  • $begingroup$
    For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
    $endgroup$
    – Mark S.
    1 hour ago
















2












$begingroup$



$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$




How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?






notation







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
    $endgroup$
    – Minus One-Twelfth
    2 hours ago












  • $begingroup$
    For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
    $endgroup$
    – Mark S.
    1 hour ago














2












2








2





$begingroup$



$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$




How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?






notation







share|cite|improve this question











$endgroup$





$$frac{n}{phi(n)}=frac{n}{nprod_{p|n}left(1-frac{1}{p}right)}=frac{1}{prod_{p|n}left(1-frac{1}{p}right)}$$




How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?






notation




notation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 1 hour ago









Robert Howard

2,0381927




2,0381927










asked 2 hours ago









Po Chen LiuPo Chen Liu

1148




1148








  • 1




    $begingroup$
    The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
    $endgroup$
    – Minus One-Twelfth
    2 hours ago












  • $begingroup$
    For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
    $endgroup$
    – Mark S.
    1 hour ago














  • 1




    $begingroup$
    The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
    $endgroup$
    – Minus One-Twelfth
    2 hours ago












  • $begingroup$
    For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
    $endgroup$
    – Mark S.
    1 hour ago








1




1




$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
2 hours ago






$begingroup$
The $phi(n)$ refers to Euler's totient function. As explained here, the $prod_{pmid n}$ refers to taking a product over all distinct primes $p$ that divide $n$.
$endgroup$
– Minus One-Twelfth
2 hours ago














$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago




$begingroup$
For symbols you don't know, you can get help from en.wikipedia.org/wiki/List_of_mathematical_symbols
$endgroup$
– Mark S.
1 hour ago










1 Answer
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$begingroup$

The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.



As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$






share|cite|improve this answer









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    1 Answer
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    1 Answer
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    5












    $begingroup$

    The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.



    As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$






    share|cite|improve this answer









    $endgroup$


















      5












      $begingroup$

      The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.



      As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$






      share|cite|improve this answer









      $endgroup$
















        5












        5








        5





        $begingroup$

        The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.



        As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$






        share|cite|improve this answer









        $endgroup$



        The big pi, $prod$ denotes a product. The subscript on this tells you which numbers this product is over. In this example, the subscript says $p|n$ which means "$p$ divides $n$" i.e. the product is over all the prime numbers $p$ that divide $n$ (the prime factors of $n$). $phi(n)$ denotes the Euler-Totient function. This counts the number of integers $m<n$ which are co-prime to $n$, i.e. have $gcd(m,n)=1$.



        As an example, say we have $n=105=3times5times7$. Then $$prod_{p|n}left(1-frac1pright)=left(1-frac13right)timesleft(1-frac15right)timesleft(1-frac17right)=frac{16}{35}$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 1 hour ago









        John DoeJohn Doe

        11.2k11238




        11.2k11238






























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