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Prove that every even perfect number is a triangular number.

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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

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edited 1 hour ago

Anirban Niloy

666218

asked 3 hours ago

Jake GJake G

442

$endgroup$

add a comment | 

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

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

share|cite|improve this question

edited 1 hour ago

Anirban Niloy

666218

asked 3 hours ago

Jake GJake G

442

$endgroup$

share|cite|improve this question

edited 1 hour ago

Anirban Niloy

666218

asked 3 hours ago

Jake GJake G

442

share|cite|improve this question

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

asked 3 hours ago

Jake GJake G

442

asked 3 hours ago

Jake GJake G

442

1 Answer
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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

answered 3 hours ago

Ross MillikanRoss Millikan

298k23198371

$endgroup$

add a comment | 

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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

answered 3 hours ago

Ross MillikanRoss Millikan

298k23198371

$endgroup$

add a comment | 

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

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.

share|cite|improve this answer

answered 3 hours ago

Ross MillikanRoss Millikan

298k23198371

$endgroup$

share|cite|improve this answer

answered 3 hours ago

Ross MillikanRoss Millikan

298k23198371

answered 3 hours ago

Ross MillikanRoss Millikan

298k23198371

answered 3 hours ago

Ross MillikanRoss Millikan

298k23198371