tag:blogger.com,1999:blog-38193052.post1735322598954415239..comments2024-03-20T08:57:17.447-03:00Comments on Jornalheiros: Matemática - 7 é o únicoPC Filhohttp://www.blogger.com/profile/16547063456626761789noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-38193052.post-6963526806916783752022-01-21T02:31:45.303-03:002022-01-21T02:31:45.303-03:00What an elegant proof. Thank you, Jake.What an elegant proof. Thank you, Jake.PC Filhohttps://www.blogger.com/profile/16547063456626761789noreply@blogger.comtag:blogger.com,1999:blog-38193052.post-54234166748503378832021-12-24T20:37:07.992-03:002021-12-24T20:37:07.992-03:00Suppose that p = n³ – 1 and n is an integer. We ca...Suppose that p = n³ – 1 and n is an integer. We can factor p as follows:<br /><br />p = n³ – 1 = (n – 1)(n² + n + 1)<br /><br />If n = 2, the first factor is 1 and the second is 7. The product of the two is 7, a prime number. However, for all integer n > 2, both factors are greater than 1. This implies that p has more than two factors and therefore is not prime. Thus 7 is the only prime number that is one less than a perfect cube.<br /><br />QEDjrh150482https://www.blogger.com/profile/10502831081969372299noreply@blogger.comtag:blogger.com,1999:blog-38193052.post-17603398031650951542021-12-24T20:36:05.640-03:002021-12-24T20:36:05.640-03:00Este comentário foi removido pelo autor.jrh150482https://www.blogger.com/profile/10502831081969372299noreply@blogger.comtag:blogger.com,1999:blog-38193052.post-56519632441491389032021-06-05T18:50:50.981-03:002021-06-05T18:50:50.981-03:00Is there an easy way to prove it?Is there an easy way to prove it?PC Filhohttps://www.blogger.com/profile/16547063456626761789noreply@blogger.com