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
    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
















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
    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














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 1 hour 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
    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




    $begingroup$
    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
    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




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
1 hour 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
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




$begingroup$
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
1






active

oldest

votes


















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









$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3123277%2fhow-do-i-break-down-the-math-symbols-in-this-equation%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    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






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3123277%2fhow-do-i-break-down-the-math-symbols-in-this-equation%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            404 Error Contact Form 7 ajax form submitting

            Image
            0 The contact form does not work, and affects loading after one try. The chrome console shows the error message: POST http://example.com/wp-json/contact-form-7/v1/contact-forms/50/feedback 404 (Not Found) send @ jquery.js?ver=1.12.4:4 ajax @ jquery.js?ver=1.12.4:4 wpcf7.submit @ scripts.js?ver=5.0.3:346 (anonymous) @ scripts.js?ver=5.0.3:53 dispatch @ jquery.js?ver=1.12.4:3 r.handle @ jquery.js?ver=1.12.4:3 How to solve this issue? thanks in advance javascript wordpress contact-form-7 share | improve this question edited Jul 17 '18 at 5:39 Kiran Shahi 4,745 3 16 43
            Read more

            How to know if a Active Directory user can login interactively

            Image
            1 I would like to know if and how is it possible to know if a AD user can login interactively (on a server) in a domain. I need to know if I can find it out using a LDAP search. Thanks. windows active-directory login user-permissions user-profile share | improve this question edited 1 hour ago yagmoth555 ♦ 11.6k 3 17 42 asked 1 hour ago Luigi Luigi 6 1 New contributor
            Read more

            TypeError: fit_transform() missing 1 required positional argument: 'X'

            Image
            0 I am trying to do Feature Scaling in a dataset, but I get an error and have no idea how to proceed: > Traceback (most recent call last): > > File "<ipython-input-10-71bea414b4d0>", line 22, in <module> > x_train = sc_X.fit_transform(x_train) > > TypeError: fit_transform() missing 1 required positional argument: 'X' and here is my code: import pandas as pd # Importing the dataset dataset = pd.read_csv('Data.csv') X = dataset.iloc[:, :-1].values y = dataset.iloc[:, 3].values # Taking care of missing data from sklearn.preprocessing import Imputer imputer = Imputer(missing_values="NaN", strategy="mean", axis=0) imputer = Imputer.fit(imputer,X[:,1:3]) X[:, 1:3] = Imputer.transform(imputer,X[
            Read more