CoolHandLouis
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 Feb 5 comment can a number of the form $x^2 + 1$ be a square number? For posterity, note that this answer evolved to be more rigorous and proof-like, which may make some "not rigorous" comments dated. The OP found the table helpful in comprehending the concept, which is why this answer was selected. Jan 17 revised can a number of the form $x^2 + 1$ be a square number? Neutral tone. Jan 17 comment can a number of the form $x^2 + 1$ be a square number? @Ramkumar - Since I did take the liberty to edit your post, please do indicate if that represents what you want to say. I'm just glad that all of us could help you! ;) Jan 17 comment can a number of the form $x^2 + 1$ be a square number? Ramkumar - I edited your post to present your reason for selecting my answer in a neutral tone since this will be viewed in the future by people who have no understanding of the dynamic issue. There is never a need to feel sorry about selecting an answer that you feel helped you. The overall general value of Allesandro's answer is evident in the points it received. Another option for you is to remove the commentary from the question, and post it as a comment under my question with an FYI to @Allesandro. Then questions and answers stand on their own and commentary is in comments. Jan 17 suggested approved edit on can a number of the form $x^2 + 1$ be a square number? Jan 17 comment can a number of the form $x^2 + 1$ be a square number? @ToddWilcox to your point about tables, I moved them to the end for a better overall presentation. Thanks. Jan 17 comment can a number of the form $x^2 + 1$ be a square number? @Mr.Brooks Point well taken, and thank you so much for the edits. It was a dynamic situation, the preface/postscript made the point needed at the time, but they are no longer relevant, so I removed them. Thanks. Jan 17 revised can a number of the form $x^2 + 1$ be a square number? Edited as per Mr. Brooks suggestion. Jan 17 revised can a number of the form $x^2 + 1$ be a square number? created more neutral tone Jan 17 revised can a number of the form $x^2 + 1$ be a square number? created more neutral tone Jan 17 comment can a number of the form $x^2 + 1$ be a square number? @ToddWilcox - Thanks for LaTeX suggestion! I don't know LaTeX, but will clean this up later when I get a chance, and will be sure to use LaTeX in future answers. Jan 17 comment can a number of the form $x^2 + 1$ be a square number? @ToddWilcox - Rigorous enough to be acceptable by whom? Note that someone even suggested that Alessandro's answer could have been more formal (rigorous)! My proof had just the right amount of rigor (not too much, not too little) to be helpful and selected as the accepted answer by the OP. The table of examples did not distract but enhanced the understanding for the OP. I think I framed this answer--including a note on levels of rigor--fairly and clearly in the Preface and Postscript. Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 11 characters in body Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 11 characters in body Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 21 characters in body Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 21 characters in body Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 21 characters in body Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 21 characters in body Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 21 characters in body Jan 15 revised can a number of the form $x^2 + 1$ be a square number? added 21 characters in body