x^2=x

S485122 · 2015-04-08, 20:37

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

R.D. Silverman · 2015-04-08, 21:11

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.

NBtarheel_33 · 2015-04-08, 21:21

Late April Fools' perhaps?

S485122 is an established participant of both GIMPS and the Mersenne Forum, so trolling seems unlikely here.

TheMawn · 2015-04-08, 21:40

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?)

R.D. Silverman · 2015-04-08, 21:55

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.

chalsall · 2015-04-08, 22:07

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....

MattcAnderson · 2015-04-08, 22:22

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

Batalov · 2015-04-08, 22:23

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..."

Brian-E · 2015-04-08, 22:38

Did the PDP 11/44 show some anomaly when computing the square of certain integers, perhaps?

Batalov · 2015-04-08, 22:51

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

fivemack · 2015-04-08, 23:06

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 ...)

2015-04-08, 20:37	#1
S485122 Sep 2006 Brussels, Belgium 2×3×281 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, 21:21	#3
NBtarheel_33 "Nathan" Jul 2008 Maryland, USA 5·223 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, 22:22	#7
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 1440₈ 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, 22:38	#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 3⁶×13 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 1100100010011₂ 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 ...)