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 2015-04-08, 20:37 #1 S485122     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
2015-04-08, 21:11   #2
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by S485122 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
Is this another troll? Worked on with a PDP 11? This is a trivial first year junior high school
algebra question.

 2015-04-08, 21:21 #3 NBtarheel_33     "Nathan" Jul 2008 Maryland, USA 111510 Posts Late April Fools' perhaps? S485122 is an established participant of both GIMPS and the Mersenne Forum, so trolling seems unlikely here.
2015-04-08, 21:40   #4
TheMawn

May 2013
East. Always East.

110101111112 Posts

Quote:
 Originally Posted by S485122 Compute the integer solutions of of the equation x^2=x.
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 non-trivial about this, it might be the question of Where Does The x = 0 Solution Go?)

Last fiddled with by TheMawn on 2015-04-08 at 21:43

2015-04-08, 21:55   #5
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by TheMawn 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 non-trivial about this, it might be the question of Where Does The x = 0 Solution Go?)
Even before one talks algebra one learns that you can't divide by 0.

2015-04-08, 22:07   #6
chalsall
If I May

"Chris Halsall"
Sep 2002

3×52×127 Posts

Quote:
 Originally Posted by R.D. Silverman Even before one talks algebra one learns that you can't divide by 0.
You can't? That's often how I get my infinity's, and sometimes my exceptions....

 2015-04-08, 22:22 #7 MattcAnderson     "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*(x-1) = 0 Then there are two solutions. x = 0 or 1. Regards, Matt
2015-04-08, 22:23   #8
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

938910 Posts

Quote:
 Originally Posted by S485122 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.)
=
Quote:
 One day in the company of friends, Hodja Nasreddin began complaining about old age. - "However, this does not impact on my strength," - he concluded suddenly. "I am just as strong as like many years ago." - "How do you know that?" - They asked him. - "In my yard, there's been a huge stone. It's been there forever. So, when I was a kid, I could not pick it up; in my youth, I also could not pick it up, and I still can not pick it up now..."

 2015-04-08, 22:38 #9 Brian-E     "Brian" Jul 2007 The Netherlands 7·467 Posts Did the PDP 11/44 show some anomaly when computing the square of certain integers, perhaps?
 2015-04-08, 22:51 #10 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100100101011012 Posts Ok, maybe the OP wanted to say, on a PDP 11/44, in a machine word, do some x2 equal x (that is, mod 232, 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
 2015-04-08, 23:06 #11 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 13·491 Posts I assumed that it meant the PDP 11/44 used some non-obvious base, but it seems to be a standard 16-bit computer and x^2=x has no extra 2-adic solutions. (the extra base-10 solutions are of course Chinese-remainder combinations of the base-2 and base-5 ones ...)