grammar in the title, then cancelled misunderstanding from my side

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edit approved Jun 14, 2015 at 9:57

Duchamp Gérard H. E.

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If $\binom{2p}{p}$ is $(-1)^{p-1} \bmod 2p+1$, is then $2p+1$ prime?

Post Reopened by Stefan Kohl♦, Lucia, YCor, Gerry Myerson, Gjergji Zaimi

occurred Jun 12, 2015 at 23:53

make the question title very specific

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edit approved Jun 12, 2015 at 19:50

Gerhard Paseman

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Is If $\binom{2p}{p}$ is $(-1)^{p-1} \bmod 2p+1$, is then $2p+1$ a prime number when some binomial satisfies a congruence?

sorry, removed typo from title. To avoid pure noise I add the context.

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edited Jun 12, 2015 at 19:17

YCor

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Is $2p+1$ is a prime number when some binomial satisfies a congruence?

Let $p$ be a positive integer; assumeif $2p+1$ is prime then it is easily checked that $$(2p+1)\mid\left(\binom{2p}{p}+(-1)^{p-1}\right)$$$$(2p+1)\mid\left(\binom{2p}{p}+(-1)^{p-1}\right);$$

conversely I conjecture that if the above divisibility assumption holds, then $2p+1$ is a prime number. Is this true?

Removed irrelevant tests and improved English and title

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edited Jun 12, 2015 at 18:56

YCor

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Post Closed as "Not suitable for this site" by Andrés E. Caicedo, GH from MO, András Bátkai, Andy Putman, Lucia

occurred Jun 12, 2015 at 17:20

edited tags

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edited Jun 12, 2015 at 17:08

GH from MO

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asked Jun 12, 2015 at 16:56

Destiny freedom

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If $\binom{2p}{p}$ is $(-1)^{p-1} \bmod 2p+1$, is then $2p+1$ prime?

Is If $\binom{2p}{p}$ is $(-1)^{p-1} \bmod 2p+1$, is then $2p+1$ a prime number when some binomial satisfies a congruence?

Is $2p+1$ is a prime number when some binomial satisfies a congruence?

Is $2p+1$ is a prime number when some binomial satisfies a congruence?

Is $2p+1$ a prime number when some binomial satisfies a congruence?