Brocard's Problem: No Solution for n! Containing Prime^2, n>7?

  • Context: Graduate 
  • Thread starter Thread starter secondprime
  • Start date Start date
Click For Summary

Discussion Overview

The discussion centers on Brocard's problem, specifically investigating integer values of n for which n! + 1 = m^2, with a focus on the condition that n! contains a prime raised to the power of exactly 2 for n > 7. Participants are examining potential proofs and results related to this problem.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant claims to have a proof that there are no solutions for n! containing a prime with power exactly 2 when n > 7, and seeks feedback on this proof.
  • Another participant humorously questions why the proof has not been shared, suggesting possible technical difficulties.
  • A participant mentions using long integer arithmetic to find no additional solutions for n < 100, aside from n = 4, 5, and 7.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are competing views regarding the existence of solutions and the validity of the proposed proof.

Contextual Notes

Limitations include the lack of detailed presentation of the proof and the specific conditions under which the claims are made, particularly regarding the nature of prime powers in factorials.

secondprime
Messages
47
Reaction score
0
Brocard's problem asks to find integer values of n for which
n! + 1 =m^2 .
where n! is the factorial.Probably I got a proof that there is no solution if n! contains a prime with power exactly 2 & n>7...looking for error...anyone else with any result?
 
Last edited:
Physics news on Phys.org
and you did not post your proof because you run out of ink? or maybe your computer crashed.
 
I have enough ink but don't know how to write with ink on computer:smile: trying to find an error in my proof,so asking about any result related to the problem.
 
Using long integer arithmetic, I found (besides n= 4, 5, 7) no other solutions for all n < 100
 

Similar threads

Graduate A Possible Proof for Brocard's Problem
  • · Replies 3 ·
Replies
3
Views
7K
Undergrad I think I've hit upon a very easy proof of impossibility of quintic
  • · Replies 2 ·
Replies
2
Views
2K
The only prime of the form n^3-1 is 7?
  • · Replies 2 ·
Replies
2
Views
4K
For n>3, show that the integers n, n+2, n+4 cannot all be prime
  • · Replies 27 ·
Replies
27
Views
4K
Graduate When n*(n+1)/2 - k is never a square
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Structure of modulo-integer matrix group GL(r,Z(n))?
  • · Replies 17 ·
Replies
17
Views
7K
Undergrad Proof that if T is Hermitian, eigenvectors form an orthonormal basis
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Is Brocard's Problem the Key to Solving Infinite Solutions?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate An argument for "Brocard's problem has finite solution"
  • · Replies 13 ·
Replies
13
Views
2K
New Idea for Prime Number Sieve
  • · Replies 36 ·
2
Replies
36
Views
2K