Prove that every even perfect number is a triangular number.even perfect numbers and primesDiscussion on even...

What is the purpose of easy combat scenarios that don't need resource expenditure?

What's the rationale behind the objections to these measures against human trafficking?

ip vs ifconfig commands pros and cons

What's a good word to describe a public place that looks like it wouldn't be rough?

Finding the number of integers that are a square and a cube at the same time

What are these green text/line displays shown during the livestream of Crew Dragon's approach to dock with the ISS?

Can chords be played on the flute?

Obtaining a matrix of complex values from associations giving the real and imaginary parts of each element?

I am on the US no-fly list. What can I do in order to be allowed on flights which go through US airspace?

Can I become debt free or should I file for bankruptcy? How do I manage my debt and finances?

Prove that every even perfect number is a triangular number.

Quenching swords in dragon blood; why?

Avoiding morning and evening handshakes

How to properly claim credit for peer review?

Why do members of Congress in committee hearings ask witnesses the same question multiple times?

How to acknowledge an embarrassing job interview, now that I work directly with the interviewer?

How to avoid being sexist when trying to employ someone to function in a very sexist environment?

Proof by Induction - New to proofs

Incompressible fluid definition

Predict mars robot position

Should I choose Itemized or Standard deduction?

Eww, those bytes are gross

Why is commutativity optional in multiplication for rings?

Why can I easily sing or whistle a tune I've just heard, but not as easily reproduce it on an instrument?



Prove that every even perfect number is a triangular number.


even perfect numbers and primesDiscussion on even and odd perfect numbers.Prove that if $2^{p}-1$ is prime then $n=2^{p-1}(2^p-1)$ is a perfect numberWhy does not the perfect number formula imply there are infinitely many perfect numbers?Relationship between Mersenne Primes and Triangular / Perfect NumbersIf n>6 is an even perfect number, Prove that n is congruent to 4 (mod12)Has it been proved that odd perfect numbers cannot be triangular?Even perfect numbers and a relationship with polygonal numbersMultiple of a Triangular Number is another Triangular NumberIf $N = prod_{i=1}^{omega(N)}{{p_i}^{alpha_i}}$ is an odd perfect number, then ${p_i}^{alpha_i} < sqrt{N}$.













1












$begingroup$


I know a triangular number is given by the formula $frac{n(n+1)}{2}$



I also know that an even perfect number is given by $2^text{n-1}(2^text{n}-1)$ if $(2^n-1)$ is prime.



Please help me to prove this.






elementary-number-theory prime-numbers







share|cite|improve this question











$endgroup$

















    1












    $begingroup$


    I know a triangular number is given by the formula $frac{n(n+1)}{2}$



    I also know that an even perfect number is given by $2^text{n-1}(2^text{n}-1)$ if $(2^n-1)$ is prime.



    Please help me to prove this.






    elementary-number-theory prime-numbers







    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      I know a triangular number is given by the formula $frac{n(n+1)}{2}$



      I also know that an even perfect number is given by $2^text{n-1}(2^text{n}-1)$ if $(2^n-1)$ is prime.



      Please help me to prove this.






      elementary-number-theory prime-numbers







      share|cite|improve this question











      $endgroup$




      I know a triangular number is given by the formula $frac{n(n+1)}{2}$



      I also know that an even perfect number is given by $2^text{n-1}(2^text{n}-1)$ if $(2^n-1)$ is prime.



      Please help me to prove this.






      elementary-number-theory prime-numbers




      elementary-number-theory prime-numbers






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 1 hour ago









      Anirban Niloy

      666218




      666218










      asked 3 hours ago









      Jake GJake G

      442




      442






















          1 Answer
          1






          active

          oldest

          votes


















          4












          $begingroup$

          You should use different variables in the two expressions. An even perfect number is then $2^{k-1}(2^k-1)$ You need to find an $n$ such that $frac 12n(n-1)=2^{k-1}(2^k-1)$. I find the right side quite suggestive.






          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%2f3134398%2fprove-that-every-even-perfect-number-is-a-triangular-number%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









            4












            $begingroup$

            You should use different variables in the two expressions. An even perfect number is then $2^{k-1}(2^k-1)$ You need to find an $n$ such that $frac 12n(n-1)=2^{k-1}(2^k-1)$. I find the right side quite suggestive.






            share|cite|improve this answer









            $endgroup$


















              4












              $begingroup$

              You should use different variables in the two expressions. An even perfect number is then $2^{k-1}(2^k-1)$ You need to find an $n$ such that $frac 12n(n-1)=2^{k-1}(2^k-1)$. I find the right side quite suggestive.






              share|cite|improve this answer









              $endgroup$
















                4












                4








                4





                $begingroup$

                You should use different variables in the two expressions. An even perfect number is then $2^{k-1}(2^k-1)$ You need to find an $n$ such that $frac 12n(n-1)=2^{k-1}(2^k-1)$. I find the right side quite suggestive.






                share|cite|improve this answer









                $endgroup$



                You should use different variables in the two expressions. An even perfect number is then $2^{k-1}(2^k-1)$ You need to find an $n$ such that $frac 12n(n-1)=2^{k-1}(2^k-1)$. I find the right side quite suggestive.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 3 hours ago









                Ross MillikanRoss Millikan

                298k23198371




                298k23198371






























                    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%2f3134398%2fprove-that-every-even-perfect-number-is-a-triangular-number%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

                    Why not use the yoke to control yaw, as well as pitch and roll? Announcing the arrival of...

                    Image
                    Does the Mueller report show a conspiracy between Russia and the Trump Campaign? Relating to the President and obstruction, were Mueller's conclusions preordained? How much damage would a cupful of neutron star matter do to the Earth? Nose gear failure in single prop aircraft: belly landing or nose landing? Should a wizard buy fine inks every time he want to copy spells into his spellbook? Can you force honesty by using the Speak with Dead and Zone of Truth spells together? A trigonometry question from STEP examination Special flights What is the "studentd" process? systemd and copy (/bin/cp): no such file or directory...
                    Read more

                    Couldn't open a raw socket. Error: Permission denied (13) (nmap)Is it possible to run networking commands...

                    Image
                    Why didn't Boeing produce its own regional jet? What is the most common color to indicate the input-field is disabled? Theorists sure want true answers to this! What is the opposite of "eschatology"? What do you call someone who asks many questions? Is there a hemisphere-neutral way of specifying a season? Is this draw by repetition? Bug? String.split chopping off empty trailing value Is it inappropriate for a student to attend their mentor's dissertation defense? How dangerous is XSS Why do I get negative height? Is it possible to map ...
                    Read more

                    VNC viewer RFB protocol error: bad desktop size 0x0I Cannot Type the Key 'd' (lowercase) in VNC Viewer...

                    Image
                    risk of flooding in petra in november How to get directions in deep space? How could a planet have erratic days? 15% tax on $7.5k earnings. Is that right? Did the UK lift the requirement for registering SIM cards? Is it allowed to activate the ability of multiple planeswalkers in a single turn? Stack Interview Code methods made from class Node and Smart Pointers Non-trope happy ending? What is the highest possible scrabble score for placing a single tile Open a doc from terminal, but not by its name The IT department bottlenecks progress, how should I handle this? ...
                    Read more