Mar12 awarded Yearling Feb19 awarded Nice Answer Feb8 awarded Good Answer Jun8 awarded Caucus May21 comment If $n$ is an odd natural number, then $8$ divides $n^{2}-1$Great, now every answer has two downvotes. Someone else (or the same person under another name?) downvoted all answers without any commenting on it. May17 awarded Nice Answer May17 comment If $n$ is an odd natural number, then $8$ divides $n^{2}-1$Whoever downvoted the answer, care to explain? May17 answered If $n$ is an odd natural number, then $8$ divides $n^{2}-1$ May10 comment A question about the fixed point and group action.I made a comment that indicates that I might be the downvoter, but I am not... So, must be someone else, who did not bother to explain. Apr25 comment Which of the following expressions completes the identity 1 + sec^2 x?@TheChaz Can you also add some cool animation? Apr25 comment Which of the following expressions completes the identity 1 + sec^2 x?Test of Math as a Foreign Language? Apr25 comment Which of the following expressions completes the identity 1 + sec^2 x?@TheChaz nice :D Apr25 comment A question about the fixed point and group action.Ok, no problem. Just to clarify. Apr25 comment A question about the fixed point and group action.@JasonDeVito Maybe something like this: if there are no 1's, then there are 5's and 7's only, but $16\equiv 1\mod 5$ while $7\equiv 2\mod 5$, so there has to be at least three 7's which is just too many. Apr25 comment A question about the fixed point and group action.You have completely rewrote your answer to the one already given by Jason DeVito in the comments, or am I missing something? Apr25 answered A Curious $\{-1,0,1\}$-valued Function on the Positive Rationals Apr24 comment How to solve this Diophantine Equation. Step by Step@Mily Why don't next time when you want to test something, instead of creating a new account and asking several similar questions in a row, you just tell people what your real problem is, and what you really want. This way, I believe, you will get more appropriate answers (I can't imagine how the two answers given here and for the other question might help to write the whole program solving Diophantine equations?!), and will also save some time for the moderators and others. Apr24 comment How to obtain all the solution for this diophantine equation? Sorry, I had no intent to criticize your answer or especially your pedagogy. And, as I said I even upvoted it. The problem at the link you gave in the comment is a completely different story. The problem at the link in the answer is (almost) exactly the same as this one. And can be solved using the exactly same method (with a little modification which you have shown in your answer). Moreover, it was asked by the same person. Apr24 comment How to obtain all the solution for this diophantine equation? @pedja You are welcome. But I still think that what you have after the "Hence" is not the best way to proceed... sorry. Because it is not immediately clear for what $k$ the last expression is integer. Or, maybe, in this case with small numbers it is clear enough... That's OK. But I would also suggest looking at the Andre Nicolas's comment above. Apr24 comment How to obtain all the solution for this diophantine equation? @pedja Ok, now there is no. :)