tag:blogger.com,1999:blog-12535639.post111704641128901919..comments2024-02-26T06:55:41.876-08:00Comments on Fermat's Last Theorem: Fermat's Last Theorem: n = 3: Step 2Larry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-12535639.post-58673420238696535012015-04-13T16:17:45.344-07:002015-04-13T16:17:45.344-07:00If f divides q^2, then it must divide q. It comes...If f divides q^2, then it must divide q. It comes from Euclid's Lemma. If f is prime and f divides ab, then f divides a or f divides b. For q^2, this means f divides q or f divides q. In other words, if a prime f divides q^2, then a prime f divides q.Larry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-73042158506924119612015-04-12T10:05:15.020-07:002015-04-12T10:05:15.020-07:00Dear sir,
I have a problem at (6). It seems to me ...Dear sir,<br />I have a problem at (6). It seems to me that f must divide q^2 and not q. And that's a problem. Ex: 9divides36 but 9 does not divide 6. It is maybe very stupid but that disturbs me.<br />Ps: sorry for my approximative english<br />Anonymoushttps://www.blogger.com/profile/16143199849107760971noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-26474707895955708202010-05-27T08:25:34.170-07:002010-05-27T08:25:34.170-07:00Hi Scouse Rob,
Thanks for noticing! I've fix...Hi Scouse Rob,<br /><br />Thanks for noticing! I've fixed the typo.<br /><br />Cheers,<br /><br />-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-75998841459547676532010-05-27T08:15:50.822-07:002010-05-27T08:15:50.822-07:00I think that there is a typo in (6), an extra '...I think that there is a typo in (6), an extra 'and'.<br /><br />I think the sentence(s) should be:<br /><br />f doesn't divide 3, since it is greater than 3. <br />So, by Euclid's Lemma, f must divide q.Scouse Robhttps://www.blogger.com/profile/00144454830208958210noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-1160410557065080452006-10-09T09:15:00.000-07:002006-10-09T09:15:00.000-07:00The reason why it can't be any power of 3 is becau...The reason why it can't be any power of 3 is because p,q are coprime.<BR/><BR/>It can be 3 since if 3 divides p (so that p=3p' but doesn't divide q, 3 is common factor of 2(3p'),(3p')^2 + 3q^2.<BR/><BR/>On the other hand, in order for 3^n to be a common factor, 3 would have to divide both p and q which is impossible since they are coprime.<BR/><BR/>-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-1146585897203231862006-05-02T09:04:00.000-07:002006-05-02T09:04:00.000-07:00Hi Daan,I looked it over and I believe that you ar...Hi Daan,<BR/><BR/>I looked it over and I believe that you are correct. I have modified the proof.<BR/><BR/>Thanks very much for noticing this!<BR/><BR/>Cheers,<BR/><BR/>-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.com