User roberto bosch cabrera - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T22:04:33Z http://mathoverflow.net/feeds/user/23528 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96362/knight-tour-prime-conjecture Knight tour prime (conjecture) Roberto Bosch Cabrera 2012-05-08T18:44:42Z 2012-11-13T19:17:55Z <p>Hello,</p> <p>I have the following conjecture:</p> <p>Write all numbers from $1$ to $n^2$ over an $n\times n$ board as usually. There not exists $n$ such that we can find a hamiltonian path on primes numbers with a knight.</p> <p>Andres Sanchez Perez (Ecole Polytechnique, Paris, France) verified this conjecture for $3\leq n \leq 100$.</p> <p>Any comments or reference will be appreciated.</p> http://mathoverflow.net/questions/96292/a-hard-diophantine-equation A hard diophantine equation Roberto Bosch Cabrera 2012-05-08T04:26:18Z 2012-05-10T01:15:36Z <p>Hello !</p> <p>I would like prove that the following diophantine equation is unsolvable: $m!+27=n^3$.</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/96292/a-hard-diophantine-equation Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-10T03:45:12Z 2012-05-10T03:45:12Z @Mark Sapir: Thank you. http://mathoverflow.net/questions/96292/a-hard-diophantine-equation Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-10T03:43:45Z 2012-05-10T03:43:45Z @GH: Thank you, your proof is amazing. http://mathoverflow.net/questions/96362/knight-tour-prime-conjecture/96391#96391 Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-09T02:19:28Z 2012-05-09T02:19:28Z @ timur:(update) Thank you, your argument is good, but you are considering that $3,5,7,11,13$ are intermediate or re-entry nodes for the hamiltonian path. What occurs if the path begin in $3$ for example?(similarly for $5,7,11,13$). http://mathoverflow.net/questions/96362/knight-tour-prime-conjecture Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-08T23:43:08Z 2012-05-08T23:43:08Z @Gerry Myerson: thanks for your new questions. http://mathoverflow.net/questions/96292/a-hard-diophantine-equation/96294#96294 Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-08T23:24:07Z 2012-05-08T23:24:07Z @GH: Thank you for your new Edit proving that $m&lt;10^{12}$. http://mathoverflow.net/questions/96362/knight-tour-prime-conjecture/96366#96366 Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-08T22:56:25Z 2012-05-08T22:56:25Z @Eric Naslund: thanks a lot for your comments. The case when $n$ is odd is easy, as you noted, I'm not wrote precisely my comment to conjecture, it must be $n$ even between $4$ and $100$, I'm sorry. Your improve to path in general is good, we need a bound for $n$ such that we can use a computer. http://mathoverflow.net/questions/96292/a-hard-diophantine-equation/96294#96294 Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-08T15:14:23Z 2012-05-08T15:14:23Z This problem arise (it is the hard part) when we try to solve the equation: $x!+y!+3=Z^3$ which was proposed as $J198$ in Mathematical Reflections. I think that the solution can be found in (1) <a href="http://www.renyi.hu/~p_erdos/1937-09.pdf" rel="nofollow">renyi.hu/~p_erdos/1937-09.pdf</a> (2) <a href="http://www.ams.org/journals/tran/2006-358-04/S0002-9947-05-03780-3/home.html" rel="nofollow">ams.org/journals/tran/2006-358-04/&hellip;</a> but I'm not sure. I'm trying to find an &quot;elementary&quot; solution. http://mathoverflow.net/questions/96292/a-hard-diophantine-equation/96294#96294 Comment by Roberto Bosch Cabrera Roberto Bosch Cabrera 2012-05-08T14:51:53Z 2012-05-08T14:51:53Z Thank you so much GH, now it is interesting find an upper bound for $m$ such that we can begin a computer search.