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

[QUOTE=S485122;399672]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[/QUOTE]

Is this another troll? Worked on with a PDP 11? This is a trivial first year junior high school
algebra question.

Late April Fools' perhaps? :unsure: S485122 is an established participant of both GIMPS and the Mersenne Forum, so trolling seems unlikely here.

[QUOTE=S485122;399672]Compute the integer solutions of of the equation x^2=x.[/QUOTE]

0, 1.

Do I win?

(EDIT: It's kind of cool though if you divide both sides by x you only get x = 1 :razz: If there was anything non-trivial about this, it might be the question of Where Does The x = 0 Solution Go?)

[QUOTE=TheMawn;399682]0, 1.

Do I win?

(EDIT: It's kind of cool though if you divide both sides by x you only get x = 1 :razz: If there was anything non-trivial about this, it might be the question of Where Does The x = 0 Solution Go?)[/QUOTE]

Even before one talks algebra one learns that you can't divide by 0.

[QUOTE=R.D. Silverman;399685]Even before one talks algebra one learns that you can't divide by 0.[/QUOTE]

You can't? That's often how I get my infinity's, and sometimes my exceptions....

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

[QUOTE=S485122;399672]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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Did the PDP 11/44 show some anomaly when computing the square of certain integers, perhaps?

Ok, maybe the OP wanted to say, on a PDP 11/44, in a machine word, do some x[SUP]2[/SUP] equal x (that is, [B]mod 2[/B][SUP]32[/SUP], 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) -- [SPOILER]there are four solutions, in decimal, ...0000000, ...00000001, ...109376, and ...890625 [/SPOILER]

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 ...)