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Old 2015-04-08, 20:37   #1
S485122
 
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Default 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
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Old 2015-04-08, 21:11   #2
R.D. Silverman
 
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Quote:
Originally Posted by S485122 View Post
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.
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Old 2015-04-08, 21:21   #3
NBtarheel_33
 
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Late April Fools' perhaps? S485122 is an established participant of both GIMPS and the Mersenne Forum, so trolling seems unlikely here.
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Old 2015-04-08, 21:40   #4
TheMawn
 
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Quote:
Originally Posted by S485122 View Post
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
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Old 2015-04-08, 21:55   #5
R.D. Silverman
 
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Quote:
Originally Posted by TheMawn View Post
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.
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Old 2015-04-08, 22:07   #6
chalsall
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Quote:
Originally Posted by R.D. Silverman View Post
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....
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Old 2015-04-08, 22:22   #7
MattcAnderson
 
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"Matthew Anderson"
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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
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Old 2015-04-08, 22:23   #8
Batalov
 
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Quote:
Originally Posted by S485122 View Post
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:
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- "However, this does not impact on my strength," - he concluded suddenly. "I am just as strong as like many years ago."
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- "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..."
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Old 2015-04-08, 22:38   #9
Brian-E
 
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Jul 2007
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Did the PDP 11/44 show some anomaly when computing the square of certain integers, perhaps?
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Old 2015-04-08, 22:51   #10
Batalov
 
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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
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Old 2015-04-08, 23:06   #11
fivemack
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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 ...)
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