tag:blogger.com,1999:blog-2433841880619171855.post7291501662957926514..comments2023-02-01T06:06:02.205+00:00Comments on Pat'sBlog: The Nuclear Age BeginsUnknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2433841880619171855.post-66315414907378668402011-03-07T11:02:49.105+00:002011-03-07T11:02:49.105+00:00Jonathon,
I'm missing something... if 2y^2 + ...Jonathon,<br /> I'm missing something... if 2y^2 + 1 is a perfect square, then it is a solution...Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-28497912097619601662011-03-06T18:15:27.335+00:002011-03-06T18:15:27.335+00:00I checked is 2y^2 + 1 a perfect square for a few n...I checked is 2y^2 + 1 a perfect square for a few numbers before encountering the second solution. Is there a way to directly generate solutions?<br /><br />JonathanAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-49499963299609864372011-03-01T20:14:13.267+00:002011-03-01T20:14:13.267+00:00Sorry Gas.., I thought it would be clear from Pell...Sorry Gas.., I thought it would be clear from Pell's name that I was looking for integer solutions where x and y are both >0... and just as a aside, I think you must have meant a hyperbola rather than ellipse. <br /><br /> For example 3,2 will work and is the smallest pair of non-negative integers (I hope) that work. <br /><br />I should have been more clear in the question.... mia culpaPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-47095279115898050102011-03-01T16:58:39.390+00:002011-03-01T16:58:39.390+00:00What do you mean "first two solutions"? ...What do you mean "first two solutions"? There is only one solution (an ellipse). If you treat each point on the ellipse as a different solution there is no ordering of them. Or did you mean the first points that occur to you, which are probably (1,0) and (-1,0)?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-81633430345775368172011-03-01T16:58:31.537+00:002011-03-01T16:58:31.537+00:00What do you mean "first two solutions"? ...What do you mean "first two solutions"? There is only one solution (an ellipse). If you treat each point on the ellipse as a different solution there is no ordering of them. Or did you mean the first points that occur to you, which are probably (1,0) and (-1,0)?Anonymousnoreply@blogger.com