If $c | b(x, y, z,…)$, does $c | b$?












0












$begingroup$


If $c$ divides something like $bxcd + bhdwou + bn$, does $ c | b$?



I'm confused because say that's true. Then let $c = 5$ and $b = 6$.



Then $c | b(10)$, but $5$ does not divide $6$.



So it this false?



If it is false, how come the solution to this, $c|abx + cby$ is true in my textbook?



edit: My bad, I was missing some info from the question, I'll delete soon










share|cite|improve this question











$endgroup$

















    0












    $begingroup$


    If $c$ divides something like $bxcd + bhdwou + bn$, does $ c | b$?



    I'm confused because say that's true. Then let $c = 5$ and $b = 6$.



    Then $c | b(10)$, but $5$ does not divide $6$.



    So it this false?



    If it is false, how come the solution to this, $c|abx + cby$ is true in my textbook?



    edit: My bad, I was missing some info from the question, I'll delete soon










    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      If $c$ divides something like $bxcd + bhdwou + bn$, does $ c | b$?



      I'm confused because say that's true. Then let $c = 5$ and $b = 6$.



      Then $c | b(10)$, but $5$ does not divide $6$.



      So it this false?



      If it is false, how come the solution to this, $c|abx + cby$ is true in my textbook?



      edit: My bad, I was missing some info from the question, I'll delete soon










      share|cite|improve this question











      $endgroup$




      If $c$ divides something like $bxcd + bhdwou + bn$, does $ c | b$?



      I'm confused because say that's true. Then let $c = 5$ and $b = 6$.



      Then $c | b(10)$, but $5$ does not divide $6$.



      So it this false?



      If it is false, how come the solution to this, $c|abx + cby$ is true in my textbook?



      edit: My bad, I was missing some info from the question, I'll delete soon







      elementary-number-theory






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 9 '18 at 5:58









      Shaun

      9,010113682




      9,010113682










      asked Dec 9 '18 at 5:47









      mingming

      3365




      3365






















          2 Answers
          2






          active

          oldest

          votes


















          0












          $begingroup$

          Hint: Let $pinBbb N$. Then $p$ is prime if and only if for all $a,binBbb N$, whenever $pmid ab$, we have either $pmid a$ or $pmid b$.






          share|cite|improve this answer









          $endgroup$





















            0












            $begingroup$

            If $(xcd + hdwou + n,c)=1$,it's true.



            More precisely, if $a|bc$ and $(a,c)=1$,then $a|b $.



            I can't comment about the textbook problem, as context is missing.






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              So the question was suppose $c|ab$ and $gcd(a, c) = 1$. Then $c = b$. So the solution did what I described up there but I'm actually still unsure why they said $c|abx + cby$ rather than $c|abx + cy$ like DIC actually says.
              $endgroup$
              – ming
              Dec 9 '18 at 6:53











            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%2f3032054%2fif-c-bx-y-z-does-c-b%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            0












            $begingroup$

            Hint: Let $pinBbb N$. Then $p$ is prime if and only if for all $a,binBbb N$, whenever $pmid ab$, we have either $pmid a$ or $pmid b$.






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              Hint: Let $pinBbb N$. Then $p$ is prime if and only if for all $a,binBbb N$, whenever $pmid ab$, we have either $pmid a$ or $pmid b$.






              share|cite|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                Hint: Let $pinBbb N$. Then $p$ is prime if and only if for all $a,binBbb N$, whenever $pmid ab$, we have either $pmid a$ or $pmid b$.






                share|cite|improve this answer









                $endgroup$



                Hint: Let $pinBbb N$. Then $p$ is prime if and only if for all $a,binBbb N$, whenever $pmid ab$, we have either $pmid a$ or $pmid b$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 9 '18 at 5:55









                ShaunShaun

                9,010113682




                9,010113682























                    0












                    $begingroup$

                    If $(xcd + hdwou + n,c)=1$,it's true.



                    More precisely, if $a|bc$ and $(a,c)=1$,then $a|b $.



                    I can't comment about the textbook problem, as context is missing.






                    share|cite|improve this answer











                    $endgroup$













                    • $begingroup$
                      So the question was suppose $c|ab$ and $gcd(a, c) = 1$. Then $c = b$. So the solution did what I described up there but I'm actually still unsure why they said $c|abx + cby$ rather than $c|abx + cy$ like DIC actually says.
                      $endgroup$
                      – ming
                      Dec 9 '18 at 6:53
















                    0












                    $begingroup$

                    If $(xcd + hdwou + n,c)=1$,it's true.



                    More precisely, if $a|bc$ and $(a,c)=1$,then $a|b $.



                    I can't comment about the textbook problem, as context is missing.






                    share|cite|improve this answer











                    $endgroup$













                    • $begingroup$
                      So the question was suppose $c|ab$ and $gcd(a, c) = 1$. Then $c = b$. So the solution did what I described up there but I'm actually still unsure why they said $c|abx + cby$ rather than $c|abx + cy$ like DIC actually says.
                      $endgroup$
                      – ming
                      Dec 9 '18 at 6:53














                    0












                    0








                    0





                    $begingroup$

                    If $(xcd + hdwou + n,c)=1$,it's true.



                    More precisely, if $a|bc$ and $(a,c)=1$,then $a|b $.



                    I can't comment about the textbook problem, as context is missing.






                    share|cite|improve this answer











                    $endgroup$



                    If $(xcd + hdwou + n,c)=1$,it's true.



                    More precisely, if $a|bc$ and $(a,c)=1$,then $a|b $.



                    I can't comment about the textbook problem, as context is missing.







                    share|cite|improve this answer














                    share|cite|improve this answer



                    share|cite|improve this answer








                    edited Dec 9 '18 at 6:06

























                    answered Dec 9 '18 at 5:56









                    Thomas ShelbyThomas Shelby

                    2,710421




                    2,710421












                    • $begingroup$
                      So the question was suppose $c|ab$ and $gcd(a, c) = 1$. Then $c = b$. So the solution did what I described up there but I'm actually still unsure why they said $c|abx + cby$ rather than $c|abx + cy$ like DIC actually says.
                      $endgroup$
                      – ming
                      Dec 9 '18 at 6:53


















                    • $begingroup$
                      So the question was suppose $c|ab$ and $gcd(a, c) = 1$. Then $c = b$. So the solution did what I described up there but I'm actually still unsure why they said $c|abx + cby$ rather than $c|abx + cy$ like DIC actually says.
                      $endgroup$
                      – ming
                      Dec 9 '18 at 6:53
















                    $begingroup$
                    So the question was suppose $c|ab$ and $gcd(a, c) = 1$. Then $c = b$. So the solution did what I described up there but I'm actually still unsure why they said $c|abx + cby$ rather than $c|abx + cy$ like DIC actually says.
                    $endgroup$
                    – ming
                    Dec 9 '18 at 6:53




                    $begingroup$
                    So the question was suppose $c|ab$ and $gcd(a, c) = 1$. Then $c = b$. So the solution did what I described up there but I'm actually still unsure why they said $c|abx + cby$ rather than $c|abx + cy$ like DIC actually says.
                    $endgroup$
                    – ming
                    Dec 9 '18 at 6:53


















                    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%2f3032054%2fif-c-bx-y-z-does-c-b%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

                    Ellipse (mathématiques)

                    Quarter-circle Tiles

                    Mont Emei