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 ${p_i}^{alpha_i} < sqrt{N}$.
$begingroup$
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
edited 1 hour ago
Anirban Niloy
666218
asked 3 hours ago
Jake GJake G
442
$endgroup$
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
edited 1 hour ago
Anirban Niloy
666218
asked 3 hours ago
Jake GJake G
442
$endgroup$
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
edited 1 hour ago
Anirban Niloy
666218
asked 3 hours ago
Jake GJake G
442
$endgroup$
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
asked 3 hours ago
Jake GJake G
442
edited 1 hour ago
Anirban Niloy
666218
asked 3 hours ago
Jake GJake G
442
edited 1 hour ago
Anirban Niloy
666218
edited 1 hour ago
Anirban Niloy
666218
edited 1 hour ago
Anirban Niloy
666218
666218
asked 3 hours ago
Jake GJake G
442
asked 3 hours ago
Jake GJake G
442
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.
answered 3 hours ago
Ross MillikanRoss Millikan
298k23198371
$endgroup$
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.
answered 3 hours ago
Ross MillikanRoss Millikan
298k23198371
$endgroup$
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.
answered 3 hours ago
Ross MillikanRoss Millikan
298k23198371
$endgroup$
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.
answered 3 hours ago
Ross MillikanRoss Millikan
298k23198371
$endgroup$
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
answered 3 hours ago
Ross MillikanRoss Millikan
298k23198371
answered 3 hours ago
Ross MillikanRoss Millikan
298k23198371
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
