tag:blogger.com,1999:blog-12535639.post116743643510925751..comments2020-05-15T21:04:01.369-07:00Comments on Fermat's Last Theorem: Van Roomen's ProblemLarry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-12535639.post-60399355426223901012007-06-09T09:40:00.000-07:002007-06-09T09:40:00.000-07:00Hi Thomas,There is a simple proof that if any solu...Hi Thomas,<BR/><BR/>There is a simple proof that if any solution exists where a,b,c are not relatively prime (that is, there is at least one prime that divides two of them), then there must exist a smaller solution that does not include that common factor. See <A HREF="http://mathrefresher.blogspot.com/2005/05/coprime-numbers-xn-yn-zn.html" REL="nofollow">here</A> for the proof.<BR/><BR/>Likewise, if a relatively prime solution exists, then there must exist an infinite number of solutions since if a^n + b^n = c^n then (m^n)(a^n) + (m^n)(b^n) = (m^n)(c^n) and (am)^n + (bm)^n = (cm)^n.<BR/><BR/>Cheers,<BR/><BR/>-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-87214252713987466982007-06-09T06:06:00.000-07:002007-06-09T06:06:00.000-07:00Dear Larry Freeman,I have visited your blog on Fer...Dear Larry Freeman,<BR/><BR/>I have visited your blog on Fermat Last theorem and very impressed with your knowledge in maths and presentation. I am an embedded software developer and I am very much interested in Maths. I have done some amateur steps for solving the FLT. I have one question:<BR/><BR/>if a^n + b^n = c^n<BR/><BR/>Then is there any proof that one of a, b or c should be prime?Thomas Judehttps://www.blogger.com/profile/04743837097251820319noreply@blogger.com