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 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
    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

            Liste der Baudenkmale in Friedland (Mecklenburg)

            Image
            In der Liste der Baudenkmale in Friedland sind alle denkmalgeschützten Bauten der Stadt Friedland (Mecklenburg-Vorpommern) und ihrer Ortsteile aufgelistet. Grundlage ist die Veröffentlichung der Denkmalliste des Landkreises Mecklenburgische Seenplatte (Auszug) vom 28. September 2016. Inhaltsverzeichnis 1 Baudenkmale nach Ortsteilen 1.1 Friedland 1.2 Bresewitz 1.3 Brohm 1.4 Cosa 1.5 Dishley 1.6 Dishley-Ausbau 1.7 Eichhorst 1.8 Glienke 1.9 Heinrichshöh 1.10 Heinrichswalde 1.11 Jatzke 1.12 Jatzke-Meierei 1.13 Liepen 1.14 Ramelow 1.15 Schwanbeck 2 Vorgesehener Denkmalbereich 3 Quelle 4 Weblinks Baudenkmale nach Ortsteilen | Friedland | ID Lage Bezeichnung Beschreibung Bild 281 An der Kleinbahn 2 Windmühle mit Umgang 282 Anklamer Straße alter Friedhof mit Portalwand 282 Anklamer Straße drei Erbbegräbnissen und Gräbern u. a. H.A. Riemann 284
            Read more

            Single-Malt-Whisky

            Image
            Fünf verschiedene schottische Single-Malt-Whiskys Als Single-Malt-Whisky oder kürzer Single Malt werden Whiskys bezeichnet, die zwei besondere Bedingungen erfüllen: Sie stammen zum ersten aus einer einzigen Brennerei, sind also kein Verschnitt aus mehreren Whiskysorten (daher Single , deutsch: einzeln). Zum zweiten wird als Getreide ausschließlich gemälzte Gerste verwendet (deswegen Malt , deutsch: Malz). Der Zusatz Single Malt wird als Prädikat verstanden, die so ausgezeichneten Whiskys sind in aller Regel besonders hochwertig. Hinzu kommt ihre besonders lange Lagerung, die Reifungszeit währt oft ein Jahrzehnt und länger. Inhaltsverzeichnis 1 Allgemeines 2 Herkunftsländer 2.1 Schottland 2.2 Irland 2.3 Japan 2.4 Kontinentaleuropa 3 Produktionsschritte 3.1 Mälzen 3.2 Brauen 3.3 Brennen 3.4 Reifung und Finish 3.5 Abfüllung 4 Altersangaben 5 Lagerung von Whiskyflaschen 6 Geschmacksklassifikation 7 Sonstig
            Read more

            Czorneboh

            Image
            Dieser Artikel erläutert den Berg Czorneboh, für die Gottheit siehe Czorneboh (Gottheit). Czorneboh Čornobóh Berggasthof mit Turm Höhe 555,7  m ü. NHN [1] Lage Freistaat Sachsen, Deutschland Gebirge Lausitzer Bergland Dominanz 15,4 km →  Kottmar Koordinaten 51° 7′ 11″  N , 14° 31′ 31″  O 51.119722222222 14.525194444444 555.7 Koordinaten: 51° 7′ 11″  N , 14° 31′ 31″  O Gestein Granodiorit Besonderheiten Aussichtsturm Czorneboh Der Czorneboh , obersorbisch Čornobóh , ist ein Berg zwischen Hochkirch und Cunewalde in der Oberlausitz. Er gehört zu der südöstlich von Bautzen gelegenen Czorneboh-Bergkette und ist mit einer Höhe von 555,7  m ü. NHN [1] der höchste Punkt dieses Ausläufers des Lausitzer Berglandes. Er leitet als Landschaftselement die wellige Granitlandschaft der Lausitzer Vorbergzone ein. Der Gipfel des Czorneboh liegt in der Gemarkung Meschwitz (Gemeinde Hochkirch), die Czornebohbaude jedoch
            Read more