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For $p$ a prime larger than $2k+2$, is it possible that $p^2$ divides $B_2k$?

2

1

$begingroup$

One characterization of the irregular primes is as follows:

For an irregular prime $p$, there exists some natural number $kle fracp-32$ such that $p$ divides [the numerator of] $B_2k$ where $B_2k$ is a Bernoulli number.

Question: Is there some prime $p$ for which there exists some natural number $kle fracp-32$, such that $p^2$ divides $B_2k$?

References that provide an answer, or just deal with the question are welcome.

number-theory elementary-number-theory reference-request prime-numbers bernoulli-numbers

share|cite|improve this question

edited Mar 27 at 21:21

J. W. Tanner

5,0551520

asked Mar 27 at 19:51

René GyRené Gy

1,230713

$endgroup$

add a comment | 

2

1

$begingroup$

One characterization of the irregular primes is as follows:

For an irregular prime $p$, there exists some natural number $kle fracp-32$ such that $p$ divides [the numerator of] $B_2k$ where $B_2k$ is a Bernoulli number.

Question: Is there some prime $p$ for which there exists some natural number $kle fracp-32$, such that $p^2$ divides $B_2k$?

References that provide an answer, or just deal with the question are welcome.

number-theory elementary-number-theory reference-request prime-numbers bernoulli-numbers

share|cite|improve this question

edited Mar 27 at 21:21

J. W. Tanner

5,0551520

asked Mar 27 at 19:51

René GyRené Gy

1,230713

$endgroup$

add a comment | 

$begingroup$

One characterization of the irregular primes is as follows:

For an irregular prime $p$, there exists some natural number $kle fracp-32$ such that $p$ divides [the numerator of] $B_2k$ where $B_2k$ is a Bernoulli number.

Question: Is there some prime $p$ for which there exists some natural number $kle fracp-32$, such that $p^2$ divides $B_2k$?

References that provide an answer, or just deal with the question are welcome.

number-theory elementary-number-theory reference-request prime-numbers bernoulli-numbers

share|cite|improve this question

edited Mar 27 at 21:21

J. W. Tanner

5,0551520

asked Mar 27 at 19:51

René GyRené Gy

1,230713

$endgroup$

share|cite|improve this question

edited Mar 27 at 21:21

J. W. Tanner

5,0551520

asked Mar 27 at 19:51

René GyRené Gy

1,230713

share|cite|improve this question

edited Mar 27 at 21:21

J. W. Tanner

5,0551520

asked Mar 27 at 19:51

René GyRené Gy

1,230713

edited Mar 27 at 21:21

J. W. Tanner

5,0551520

edited Mar 27 at 21:21

J. W. Tanner

5,0551520

asked Mar 27 at 19:51

René GyRené Gy

1,230713

asked Mar 27 at 19:51

René GyRené Gy

1,230713