I have tried to think as intersections of two lines but for $2x+3$ and $5x+7$ is failed to have integer intersections (but not sure it is enough counterexample). Is the above generalisation correct? Can you give a counter-example, or a hint for how to prove it?
We want to find the solution $x$ to the congruence system  $$\begin{align} x &amp;\equiv r_1 \!\!\!\pmod{\!m_1}\\ x &amp;\equiv r_2 \!\!\!\pmod{\!m_2}\end{align},\ \ {\rm where}\ \  \gcd(m_1, m_2) = 1$$  These can be rewritten as  $$\begin{align} x &amp;= r_1 + m_1 j\\ x &amp;= r_2 - m_2k\end{align}$$  for unknown integers $j, k$. So we set those two equations as equal and rearrange them to  $$m_1j + m_2k = r_2 - r_1$$  Now assume we perform $\text{egcd}(m_1, m_2)$, which gives us the solution to  $$m_1u + m_2v = \gcd(m_1, m_2)$$  Let the integer $\,h\,$ make $\,h \gcd(m_1, m_2) = r_2 - r_1$.  Then $\qquad hm_1u + hm_2v = h\gcd(m_1, m_2) =  r_2 - r_1 = m_1j + m_2k$  At this point I am lost because I don't think we can just assume  $hm_1u = m_1j$ and extract $j = hu$.   How do I get the values of $j$ or $k$ so I can get the value of $x$?
According to , the only restriction on self-deleting an answer is that you can't delete an answer that's been accepted.  But I've also heard of users getting in trouble for deleting (non-accepted) answers, and there's the CC-SA license to consider, so -- quite aside from what is technically possible -- my question is when it's permitted to delete your own answer.  Some cases to consider:   You now believe the answer is incorrect. Your answer is correct, but another answer covers the same territory better. You aren't satisfied with the quality/rigor of your answer, e.g. it's speculative and you didn't back it up (on a site that expects that). Something in the answer embarrasses you and you'd rather just make it go away. Your answer wasn't well-received by the community (whether that's "meh" or "make the rep bleeding stop please"). (I'm sure there are others; this isn't meant to be an exhaustive list.)   Does voting matter, either in absolute terms or in comparison to other answers?  For example, maybe it's ok to delete a lower-voted one but not the top-voted answer, or one with score > N??  There is a badge, Disciplined, for deleting your own post of score 3 or higher.  This tells me that it's sometimes ok to delete upvoted answers.  But I'm not sure how much policy we can infer from badges.  Could we have some clarification please? Getting ssh to execute a command in the background on target machine I'm trying to migrate a MySQL-based app over to Microsoft SQL Server 2005 (not by choice, but that's life).  In the original app, we used almost entirely ANSI-SQL compliant statements, with one significant exception -- we used MySQL's group_concat function fairly frequently.  group_concat, by the way, does this: given a table of, say, employee names and projects...  SELECT empName, projID FROM project_members;   returns:  ANDY   |  A100 ANDY   |  B391 ANDY   |  X010 TOM    |  A100 TOM    |  A510   ... and here's what you get with group_concat:  SELECT      empName, group_concat(projID SEPARATOR ' / ')  FROM      project_members  GROUP BY      empName;   returns:  ANDY   |  A100 / B391 / X010 TOM    |  A100 / A510   So what I'd like to know is: Is it possible to write, say, a user-defined function in SQL Server which emulates the functionality of group_concat?   I have almost no experience using UDFs, stored procedures, or anything like that, just straight-up SQL, so please err on the side of too much explanation :) One hour Lufthansa transit time in Frankfurt from Bangalore to Dublin Problems with partial derivatives. I'm trying to write a program in C (on Linux) that loops until the user presses a key, but shouldn't require a keypress to continue each loop.  Is there a simple way to do this? 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If $x>0$, $\,x^{1/n}$ tends to $1$ as $n\to\infty$ I am looking for a proof possibly using the sandwich theorem and/or Bernoulli's inequality for proving the following statement:  If $x&gt;0$ then $x^{1/n}$ tends to $1$. Drift velocity in Drude model