Prove that every even perfect number is a triangular number.
$begingroup$
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
$endgroup$
add a comment |
$begingroup$
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
$endgroup$
add a comment |
$begingroup$
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
$endgroup$
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
edited 1 hour ago
Anirban Niloy
666218
666218
asked 3 hours ago
Jake GJake G
442
442
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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.
$endgroup$
add a comment |
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
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
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.
answered 3 hours ago
Ross MillikanRoss Millikan
298k23198371
298k23198371
add a comment |
add a comment |
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.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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