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Brocard's problem: positive integers n such that n!+1 = m^2.
(history; published version)
#39 by Charles R Greathouse IV at Thu Sep 08 08:45:38 EDT 2022
PROG

(MAGMAMagma) [ <n, p>: n in [1..8047] | t where t, p:=IsSquare(Factorial(n)+1) ]; // Klaus Brockhaus, Nov 05 2008

Discussion
Thu Sep 08
08:45
OEIS Server: https://oeis.org/edit/global/2944
#38 by Michael Somos at Thu Feb 14 23:36:06 EST 2019
STATUS

proposed

approved

#37 by Michel Marcus at Wed Jan 09 12:18:26 EST 2019
STATUS

editing

proposed

#36 by Michel Marcus at Wed Jan 09 12:18:18 EST 2019
LINKS

Apoloniusz Tyszka, <a href="https://philarchive.org/rec/TYSDAS">On sets X subset of N for which we know an algorithm that computes a threshold number t(X) \in N such that X is infinite if and only if X contains an element greater than t(X)</a>, 2019.

STATUS

proposed

editing

Discussion
Wed Jan 09
12:18
Michel Marcus: \in
#35 by Apoloniusz Tyszka at Wed Jan 09 11:43:18 EST 2019
STATUS

editing

proposed

#34 by Apoloniusz Tyszka at Wed Jan 09 11:42:28 EST 2019
LINKS

Apoloniusz Tyszka, <a href="https://philarchive.org/rec/TYSDAS">On sets X \subseteq \mathbb{subset of N} for which we know an algorithm that computes a threshold number t(X) \in \mathbb{N} such that X is infinite if and only if X contains an element greater than t(X)</a>, 2019.

#33 by Michel Marcus at Tue Jan 08 09:48:14 EST 2019
LINKS

Eric Weisstein, Eric W. 's World of Mathematics, <a href="http://mathworld.wolfram.com/BrocardsProblem.html">Brocard's Problem</a>.

#32 by Michel Marcus at Tue Jan 08 09:47:58 EST 2019
LINKS

Berndt, B. C. and Galway, W. F. <a href="http://www.math.uiuc.edu/~berndt/articles/galway.pdf">On the Brocard-Ramanujan Diophantine Equation n!+1=m^2</a>, The Ramanujan Journal, March 2000, Volume 4, Issue 1, pp 41-42. H% Apoloniusz Tyszka, <a href="https://philarchive.org/rec/TYSDAS">On sets X \subseteq \mathbb{N} for which we know an algorithm that computes a threshold number t(X) \in \mathbb{N} such that X is infinite if and only if X contains an element greater than t(X).</a> 2019.

Apoloniusz Tyszka, <a href="https://philarchive.org/rec/TYSDAS">On sets X \subseteq \mathbb{N} for which we know an algorithm that computes a threshold number t(X) \in \mathbb{N} such that X is infinite if and only if X contains an element greater than t(X)</a>, 2019.

STATUS

proposed

editing

#31 by Apoloniusz Tyszka at Tue Jan 08 07:31:03 EST 2019
STATUS

editing

proposed

Discussion
Tue Jan 08
09:47
Michel Marcus: and same comment about link title
#30 by Apoloniusz Tyszka at Tue Jan 08 07:30:56 EST 2019
LINKS

Berndt, B. C. and Galway, W. F. <a href="http://www.math.uiuc.edu/~berndt/articles/galway.pdf">On the Brocard-Ramanujan Diophantine Equation n!+1=m^2</a>, The Ramanujan Journal, March 2000, Volume 4, Issue 1, pp 41-42. H% Apoloniusz Tyszka, <a href="https://philarchive.org/rec/TYSDAS">On sets X \subseteq \mathbb{N} for which we know an algorithm that computes a threshold number t(X) \in \mathbb{N} such that X is infinite if and only if X contains an element greater than t(X).</a> 2019.

STATUS

proposed

editing