20150408, 20:37  #1 
Sep 2006
Brussels, Belgium
3×7×79 Posts 
x^2=x
A bit late.
A problem I worked upon some 30 years ago on a PDP 11/44 : Compute the integer solutions of of the equation x^2=x. I tried to find by searching the internet, but I found no trace of this (probably I did not search well.) Jacob 
20150408, 21:11  #2  
Nov 2003
2^{2}×5×373 Posts 
Quote:
algebra question. 

20150408, 21:21  #3 
"Nathan"
Jul 2008
Maryland, USA
1115_{10} Posts 
Late April Fools' perhaps? S485122 is an established participant of both GIMPS and the Mersenne Forum, so trolling seems unlikely here.

20150408, 21:40  #4 
May 2013
East. Always East.
11010111111_{2} Posts 
0, 1.
Do I win? (EDIT: It's kind of cool though if you divide both sides by x you only get x = 1 If there was anything nontrivial about this, it might be the question of Where Does The x = 0 Solution Go?) Last fiddled with by TheMawn on 20150408 at 21:43 
20150408, 21:55  #5 
Nov 2003
2^{2}×5×373 Posts 
Even before one talks algebra one learns that you can't divide by 0.

20150408, 22:07  #6 
If I May
"Chris Halsall"
Sep 2002
Barbados
3×5^{2}×127 Posts 

20150408, 22:22  #7 
"Matthew Anderson"
Dec 2010
Oregon, USA
2·3·7·17 Posts 
Start with x^2 = x
Subtract x from both sides x^2  x = 0 Factor out an x x*(x1) = 0 Then there are two solutions. x = 0 or 1. Regards, Matt 
20150408, 22:23  #8  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9389_{10} Posts 
Quote:
Quote:


20150408, 22:38  #9 
"Brian"
Jul 2007
The Netherlands
7·467 Posts 
Did the PDP 11/44 show some anomaly when computing the square of certain integers, perhaps?

20150408, 22:51  #10 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010010101101_{2} Posts 
Ok, maybe the OP wanted to say, on a PDP 11/44, in a machine word, do some x^{2} equal x (that is, mod 2^{32}, for example)?
This is akin to a perenially popular search for a ...x which squared still ends with ...x (in a certain base, e.g. in decimal)  there are four solutions, in decimal, ...0000000, ...00000001, ...109376, and ...890625 
20150408, 23:06  #11 
(loop (#_fork))
Feb 2006
Cambridge, England
13·491 Posts 
I assumed that it meant the PDP 11/44 used some nonobvious base, but it seems to be a standard 16bit computer and x^2=x has no extra 2adic solutions.
(the extra base10 solutions are of course Chineseremainder combinations of the base2 and base5 ones ...) 